/* Copyright 2002-2021 CS GROUP
    * Licensed to CS GROUP (CS) under one or more
    * contributor license agreements.  See the NOTICE file distributed with
    * this work for additional information regarding copyright ownership.
    * CS licenses this file to You under the Apache License, Version 2.0
    * (the "License"); you may not use this file except in compliance with
    * the License.  You may obtain a copy of the License at
    *
    *   http://www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
   * limitations under the License.
   */
  package org.orekit.propagation.analytical;
  
  import java.util.Collections;
  import java.util.List;
  
  import org.hipparchus.Field;
  import org.hipparchus.CalculusFieldElement;
  import org.hipparchus.analysis.differentiation.FieldUnivariateDerivative2;
  import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
  import org.hipparchus.util.FastMath;
  import org.hipparchus.util.FieldSinCos;
  import org.hipparchus.util.MathArrays;
  import org.hipparchus.util.MathUtils;
  import org.orekit.attitudes.AttitudeProvider;
  import org.orekit.attitudes.InertialProvider;
  import org.orekit.errors.OrekitException;
  import org.orekit.errors.OrekitMessages;
  import org.orekit.forces.gravity.potential.UnnormalizedSphericalHarmonicsProvider;
  import org.orekit.forces.gravity.potential.UnnormalizedSphericalHarmonicsProvider.UnnormalizedSphericalHarmonics;
  import org.orekit.orbits.FieldCartesianOrbit;
  import org.orekit.orbits.FieldCircularOrbit;
  import org.orekit.orbits.FieldOrbit;
  import org.orekit.orbits.OrbitType;
  import org.orekit.orbits.PositionAngle;
  import org.orekit.propagation.FieldSpacecraftState;
  import org.orekit.propagation.PropagationType;
  import org.orekit.time.FieldAbsoluteDate;
  import org.orekit.utils.FieldTimeSpanMap;
  import org.orekit.utils.ParameterDriver;
  import org.orekit.utils.TimeStampedFieldPVCoordinates;
  
  /** This class propagates a {@link org.orekit.propagation.FieldSpacecraftState}
   *  using the analytical Eckstein-Hechler model.
   * <p>The Eckstein-Hechler model is suited for near circular orbits
   * (e &lt; 0.1, with poor accuracy between 0.005 and 0.1) and inclination
   * neither equatorial (direct or retrograde) nor critical (direct or
   * retrograde).</p>
   * @see FieldOrbit
   * @author Guylaine Prat
   */
  public class FieldEcksteinHechlerPropagator<T extends CalculusFieldElement<T>> extends FieldAbstractAnalyticalPropagator<T> {
  
      /** Initial Eckstein-Hechler model. */
      private FieldEHModel<T> initialModel;
  
      /** All models. */
      private transient FieldTimeSpanMap<FieldEHModel<T>, T> models;
  
      /** Reference radius of the central body attraction model (m). */
      private double referenceRadius;
  
      /** Central attraction coefficient (m³/s²). */
      private T mu;
  
      /** Un-normalized zonal coefficients. */
      private double[] ck0;
  
      /** Build a propagator from FieldOrbit and potential provider.
       * <p>Mass and attitude provider are set to unspecified non-null arbitrary values.</p>
       *
       * <p>Using this constructor, an initial osculating orbit is considered.</p>
       *
       * @param initialOrbit initial FieldOrbit
       * @param provider for un-normalized zonal coefficients
       * @see #FieldEcksteinHechlerPropagator(FieldOrbit, AttitudeProvider,
       * UnnormalizedSphericalHarmonicsProvider)
       * @see #FieldEcksteinHechlerPropagator(FieldOrbit, UnnormalizedSphericalHarmonicsProvider,
       * PropagationType)
       */
      public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit,
                                            final UnnormalizedSphericalHarmonicsProvider provider) {
          this(initialOrbit, InertialProvider.of(initialOrbit.getFrame()),
               initialOrbit.getA().getField().getZero().add(DEFAULT_MASS), provider,
               provider.onDate(initialOrbit.getDate().toAbsoluteDate()));
      }
  
      /**
       * Private helper constructor.
       * <p>Using this constructor, an initial osculating orbit is considered.</p>
       * @param initialOrbit initial FieldOrbit
       * @param attitude attitude provider
       * @param mass spacecraft mass
       * @param provider for un-normalized zonal coefficients
      * @param harmonics {@code provider.onDate(initialOrbit.getDate())}
      * @see #FieldEcksteinHechlerPropagator(FieldOrbit, AttitudeProvider, CalculusFieldElement,
      * UnnormalizedSphericalHarmonicsProvider, UnnormalizedSphericalHarmonicsProvider.UnnormalizedSphericalHarmonics, PropagationType)
      */
     public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit,
                                           final  AttitudeProvider attitude,
                                           final T mass,
                                           final UnnormalizedSphericalHarmonicsProvider provider,
                                           final UnnormalizedSphericalHarmonicsProvider.UnnormalizedSphericalHarmonics harmonics) {
         this(initialOrbit, attitude,  mass, provider.getAe(), initialOrbit.getA().getField().getZero().add(provider.getMu()),
              harmonics.getUnnormalizedCnm(2, 0),
              harmonics.getUnnormalizedCnm(3, 0),
              harmonics.getUnnormalizedCnm(4, 0),
              harmonics.getUnnormalizedCnm(5, 0),
              harmonics.getUnnormalizedCnm(6, 0));
     }
 
     /** Build a propagator from FieldOrbit and potential.
      * <p>Mass and attitude provider are set to unspecified non-null arbitrary values.</p>
      * <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
      * are related to both the normalized coefficients
      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
      *  and the J<sub>n</sub> one as follows:
      * <p>
      *   C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
      *                      <span style="text-decoration: overline">C</span><sub>n,0</sub>
      * <p>
      *   C<sub>n,0</sub> = -J<sub>n</sub>
      *
      * <p>Using this constructor, an initial osculating orbit is considered.</p>
      *
      * @param initialOrbit initial FieldOrbit
      * @param referenceRadius reference radius of the Earth for the potential model (m)
      * @param mu central attraction coefficient (m³/s²)
      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
      * @param c60 un-normalized zonal coefficient (about -5.41e-7 for Earth)
      * @see org.orekit.utils.Constants
      * @see #FieldEcksteinHechlerPropagator(FieldOrbit, AttitudeProvider, double,
      * CalculusFieldElement, double, double, double, double, double)
      */
     public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit,
                                           final double referenceRadius, final T mu,
                                           final double c20, final double c30, final double c40,
                                           final double c50, final double c60) {
         this(initialOrbit, InertialProvider.of(initialOrbit.getFrame()),
              initialOrbit.getDate().getField().getZero().add(DEFAULT_MASS),
              referenceRadius, mu, c20, c30, c40, c50, c60);
     }
 
     /** Build a propagator from FieldOrbit, mass and potential provider.
      * <p>Attitude law is set to an unspecified non-null arbitrary value.</p>
      *
      * <p>Using this constructor, an initial osculating orbit is considered.</p>
      *
      * @param initialOrbit initial FieldOrbit
      * @param mass spacecraft mass
      * @param provider for un-normalized zonal coefficients
      * @see #FieldEcksteinHechlerPropagator(FieldOrbit, AttitudeProvider,
      * CalculusFieldElement, UnnormalizedSphericalHarmonicsProvider)
      */
     public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit, final T mass,
                                           final UnnormalizedSphericalHarmonicsProvider provider) {
         this(initialOrbit, InertialProvider.of(initialOrbit.getFrame()),
                 mass, provider, provider.onDate(initialOrbit.getDate().toAbsoluteDate()));
     }
 
     /** Build a propagator from FieldOrbit, mass and potential.
      * <p>Attitude law is set to an unspecified non-null arbitrary value.</p>
      * <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
      * are related to both the normalized coefficients
      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
      *  and the J<sub>n</sub> one as follows:</p>
      * <p>
      *   C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
      *                      <span style="text-decoration: overline">C</span><sub>n,0</sub>
      * <p>
      *   C<sub>n,0</sub> = -J<sub>n</sub>
      *
      * <p>Using this constructor, an initial osculating orbit is considered.</p>
      *
      * @param initialOrbit initial FieldOrbit
      * @param mass spacecraft mass
      * @param referenceRadius reference radius of the Earth for the potential model (m)
      * @param mu central attraction coefficient (m³/s²)
      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
      * @param c60 un-normalized zonal coefficient (about -5.41e-7 for Earth)
      * @see #FieldEcksteinHechlerPropagator(FieldOrbit, AttitudeProvider,
      * CalculusFieldElement, double, CalculusFieldElement, double, double, double, double, double)
      */
     public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit, final T mass,
                                           final double referenceRadius, final T mu,
                                           final double c20, final double c30, final double c40,
                                           final double c50, final double c60) {
         this(initialOrbit, InertialProvider.of(initialOrbit.getFrame()),
                 mass, referenceRadius, mu, c20, c30, c40, c50, c60);
     }
 
     /** Build a propagator from FieldOrbit, attitude provider and potential provider.
      * <p>Mass is set to an unspecified non-null arbitrary value.</p>
      * <p>Using this constructor, an initial osculating orbit is considered.</p>
      * @param initialOrbit initial FieldOrbit
      * @param attitudeProv attitude provider
      * @param provider for un-normalized zonal coefficients
      */
     public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit,
                                           final AttitudeProvider attitudeProv,
                                           final UnnormalizedSphericalHarmonicsProvider provider) {
         this(initialOrbit, attitudeProv, initialOrbit.getA().getField().getZero().add(DEFAULT_MASS), provider, provider.onDate(initialOrbit.getDate().toAbsoluteDate()));
     }
 
     /** Build a propagator from FieldOrbit, attitude provider and potential.
      * <p>Mass is set to an unspecified non-null arbitrary value.</p>
      * <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
      * are related to both the normalized coefficients
      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
      *  and the J<sub>n</sub> one as follows:</p>
      * <p>
      *   C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
      *                     <span style="text-decoration: overline">C</span><sub>n,0</sub>
      * <p>
      *   C<sub>n,0</sub> = -J<sub>n</sub>
      *
      * <p>Using this constructor, an initial osculating orbit is considered.</p>
      *
      * @param initialOrbit initial FieldOrbit
      * @param attitudeProv attitude provider
      * @param referenceRadius reference radius of the Earth for the potential model (m)
      * @param mu central attraction coefficient (m³/s²)
      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
      * @param c60 un-normalized zonal coefficient (about -5.41e-7 for Earth)
      */
     public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit,
                                           final AttitudeProvider attitudeProv,
                                           final double referenceRadius, final T mu,
                                           final double c20, final double c30, final double c40,
                                           final double c50, final double c60) {
         this(initialOrbit, attitudeProv, initialOrbit.getDate().getField().getZero().add(DEFAULT_MASS),
              referenceRadius, mu, c20, c30, c40, c50, c60);
     }
 
     /** Build a propagator from FieldOrbit, attitude provider, mass and potential provider.
      * <p>Using this constructor, an initial osculating orbit is considered.</p>
      * @param initialOrbit initial FieldOrbit
      * @param attitudeProv attitude provider
      * @param mass spacecraft mass
      * @param provider for un-normalized zonal coefficients
      * @see #FieldEcksteinHechlerPropagator(FieldOrbit, AttitudeProvider, CalculusFieldElement,
      * UnnormalizedSphericalHarmonicsProvider, PropagationType)
      */
     public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit,
                                           final AttitudeProvider attitudeProv,
                                           final T mass,
                                           final UnnormalizedSphericalHarmonicsProvider provider) {
         this(initialOrbit, attitudeProv, mass, provider, provider.onDate(initialOrbit.getDate().toAbsoluteDate()));
     }
 
     /** Build a propagator from FieldOrbit, attitude provider, mass and potential.
      * <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
      * are related to both the normalized coefficients
      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
      *  and the J<sub>n</sub> one as follows:</p>
      * <p>
      *   C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
      *                      <span style="text-decoration: overline">C</span><sub>n,0</sub>
      * <p>
      *   C<sub>n,0</sub> = -J<sub>n</sub>
      *
      * <p>Using this constructor, an initial osculating orbit is considered.</p>
      *
      * @param initialOrbit initial FieldOrbit
      * @param attitudeProv attitude provider
      * @param mass spacecraft mass
      * @param referenceRadius reference radius of the Earth for the potential model (m)
      * @param mu central attraction coefficient (m³/s²)
      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
      * @param c60 un-normalized zonal coefficient (about -5.41e-7 for Earth)
      * @see #FieldEcksteinHechlerPropagator(FieldOrbit, AttitudeProvider, CalculusFieldElement, double,
      *                                      CalculusFieldElement, double, double, double, double, double, PropagationType)
      */
     public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit,
                                           final AttitudeProvider attitudeProv,
                                           final T mass,
                                           final double referenceRadius, final T mu,
                                           final double c20, final double c30, final double c40,
                                           final double c50, final double c60) {
         this(initialOrbit, attitudeProv, mass, referenceRadius, mu, c20, c30, c40, c50, c60, PropagationType.OSCULATING);
     }
 
     /** Build a propagator from orbit and potential provider.
      * <p>Mass and attitude provider are set to unspecified non-null arbitrary values.</p>
      *
      * <p>Using this constructor, it is possible to define the initial orbit as
      * a mean Eckstein-Hechler orbit or an osculating one.</p>
      *
      * @param initialOrbit initial orbit
      * @param provider for un-normalized zonal coefficients
      * @param initialType initial orbit type (mean Eckstein-Hechler orbit or osculating orbit)
      * @since 10.2
      */
     public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit,
                                           final UnnormalizedSphericalHarmonicsProvider provider,
                                           final PropagationType initialType) {
         this(initialOrbit, InertialProvider.of(initialOrbit.getFrame()),
              initialOrbit.getA().getField().getZero().add(DEFAULT_MASS), provider,
              provider.onDate(initialOrbit.getDate().toAbsoluteDate()), initialType);
     }
 
     /** Build a propagator from orbit, attitude provider, mass and potential provider.
      * <p>Using this constructor, it is possible to define the initial orbit as
      * a mean Eckstein-Hechler orbit or an osculating one.</p>
      * @param initialOrbit initial orbit
      * @param attitudeProv attitude provider
      * @param mass spacecraft mass
      * @param provider for un-normalized zonal coefficients
      * @param initialType initial orbit type (mean Eckstein-Hechler orbit or osculating orbit)
      * @since 10.2
      */
     public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit,
                                           final AttitudeProvider attitudeProv,
                                           final T mass,
                                           final UnnormalizedSphericalHarmonicsProvider provider,
                                           final PropagationType initialType) {
         this(initialOrbit, attitudeProv, mass, provider, provider.onDate(initialOrbit.getDate().toAbsoluteDate()), initialType);
     }
 
     /**
      * Private helper constructor.
      * <p>Using this constructor, it is possible to define the initial orbit as
      * a mean Eckstein-Hechler orbit or an osculating one.</p>
      * @param initialOrbit initial orbit
      * @param attitude attitude provider
      * @param mass spacecraft mass
      * @param provider for un-normalized zonal coefficients
      * @param harmonics {@code provider.onDate(initialOrbit.getDate())}
      * @param initialType initial orbit type (mean Eckstein-Hechler orbit or osculating orbit)
      * @since 10.2
      */
     public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit,
                                           final AttitudeProvider attitude,
                                           final T mass,
                                           final UnnormalizedSphericalHarmonicsProvider provider,
                                           final UnnormalizedSphericalHarmonics harmonics,
                                           final PropagationType initialType) {
         this(initialOrbit, attitude, mass, provider.getAe(), initialOrbit.getA().getField().getZero().add(provider.getMu()),
              harmonics.getUnnormalizedCnm(2, 0),
              harmonics.getUnnormalizedCnm(3, 0),
              harmonics.getUnnormalizedCnm(4, 0),
              harmonics.getUnnormalizedCnm(5, 0),
              harmonics.getUnnormalizedCnm(6, 0),
              initialType);
     }
 
     /** Build a propagator from FieldOrbit, attitude provider, mass and potential.
      * <p>The C<sub>n,0</sub> coefficients are the denormalized zonal coefficients, they
      * are related to both the normalized coefficients
      * <span style="text-decoration: overline">C</span><sub>n,0</sub>
      *  and the J<sub>n</sub> one as follows:</p>
      * <p>
      *   C<sub>n,0</sub> = [(2-δ<sub>0,m</sub>)(2n+1)(n-m)!/(n+m)!]<sup>½</sup>
      *                      <span style="text-decoration: overline">C</span><sub>n,0</sub>
      * <p>
      *   C<sub>n,0</sub> = -J<sub>n</sub>
      *
      * <p>Using this constructor, it is possible to define the initial orbit as
      * a mean Eckstein-Hechler orbit or an osculating one.</p>
      *
      * @param initialOrbit initial FieldOrbit
      * @param attitudeProv attitude provider
      * @param mass spacecraft mass
      * @param referenceRadius reference radius of the Earth for the potential model (m)
      * @param mu central attraction coefficient (m³/s²)
      * @param c20 un-normalized zonal coefficient (about -1.08e-3 for Earth)
      * @param c30 un-normalized zonal coefficient (about +2.53e-6 for Earth)
      * @param c40 un-normalized zonal coefficient (about +1.62e-6 for Earth)
      * @param c50 un-normalized zonal coefficient (about +2.28e-7 for Earth)
      * @param c60 un-normalized zonal coefficient (about -5.41e-7 for Earth)
      * @param initialType initial orbit type (mean Eckstein-Hechler orbit or osculating orbit)
      * @since 10.2
      */
     public FieldEcksteinHechlerPropagator(final FieldOrbit<T> initialOrbit,
                                           final AttitudeProvider attitudeProv,
                                           final T mass,
                                           final double referenceRadius, final T mu,
                                           final double c20, final double c30, final double c40,
                                           final double c50, final double c60,
                                           final PropagationType initialType) {
 
         super(mass.getField(), attitudeProv);
         try {
 
             // store model coefficients
             this.referenceRadius = referenceRadius;
             this.mu  = mu;
             this.ck0 = new double[] {
                 0.0, 0.0, c20, c30, c40, c50, c60
             };
 
             // compute mean parameters if needed
             // transform into circular adapted parameters used by the Eckstein-Hechler model
             resetInitialState(new FieldSpacecraftState<>(initialOrbit,
                                                          attitudeProv.getAttitude(initialOrbit,
                                                                                   initialOrbit.getDate(),
                                                                                   initialOrbit.getFrame()),
                                                          mass),
                               initialType);
 
         } catch (OrekitException oe) {
             throw new OrekitException(oe);
         }
     }
 
     /** {@inheritDoc}
      * <p>The new initial state to consider
      * must be defined with an osculating orbit.</p>
      * @see #resetInitialState(FieldSpacecraftState, PropagationType)
      */
     @Override
     public void resetInitialState(final FieldSpacecraftState<T> state) {
         resetInitialState(state, PropagationType.OSCULATING);
     }
 
     /** Reset the propagator initial state.
      * @param state new initial state to consider
      * @param stateType mean Eckstein-Hechler orbit or osculating orbit
      * @since 10.2
      */
     public void resetInitialState(final FieldSpacecraftState<T> state, final PropagationType stateType) {
         super.resetInitialState(state);
         final FieldCircularOrbit<T> circular = (FieldCircularOrbit<T>) OrbitType.CIRCULAR.convertType(state.getOrbit());
         this.initialModel = (stateType == PropagationType.MEAN) ?
                              new FieldEHModel<>(circular, state.getMass(), referenceRadius, mu, ck0) :
                              computeMeanParameters(circular, state.getMass());
         this.models = new FieldTimeSpanMap<FieldEHModel<T>, T>(initialModel, state.getA().getField());
     }
 
     /** {@inheritDoc} */
     @Override
     protected void resetIntermediateState(final FieldSpacecraftState<T> state, final boolean forward) {
         final FieldEHModel<T> newModel = computeMeanParameters((FieldCircularOrbit<T>) OrbitType.CIRCULAR.convertType(state.getOrbit()),
                                                        state.getMass());
         if (forward) {
             models.addValidAfter(newModel, state.getDate());
         } else {
             models.addValidBefore(newModel, state.getDate());
         }
         stateChanged(state);
     }
 
     /** Compute mean parameters according to the Eckstein-Hechler analytical model.
      * @param osculating osculating FieldOrbit
      * @param mass constant mass
      * @return Eckstein-Hechler mean model
      */
     private FieldEHModel<T> computeMeanParameters(final FieldCircularOrbit<T> osculating, final T mass) {
 
         // sanity check
         if (osculating.getA().getReal() < referenceRadius) {
             throw new OrekitException(OrekitMessages.TRAJECTORY_INSIDE_BRILLOUIN_SPHERE,
                                            osculating.getA());
         }
         final Field<T> field = mass.getField();
         final T one = field.getOne();
         final T zero = field.getZero();
         // rough initialization of the mean parameters
         FieldEHModel<T> current = new FieldEHModel<>(osculating, mass, referenceRadius, mu, ck0);
         // threshold for each parameter
         final T epsilon         = one.multiply(1.0e-13);
         final T thresholdA      = epsilon.multiply(current.mean.getA().abs().add(1.0));
         final T thresholdE      = epsilon.multiply(current.mean.getE().add(1.0));
         final T thresholdAngles = epsilon.multiply(one.getPi());
 
 
         int i = 0;
         while (i++ < 100) {
 
             // recompute the osculating parameters from the current mean parameters
             final FieldUnivariateDerivative2<T>[] parameters = current.propagateParameters(current.mean.getDate());
             // adapted parameters residuals
             final T deltaA      = osculating.getA()         .subtract(parameters[0].getValue());
             final T deltaEx     = osculating.getCircularEx().subtract(parameters[1].getValue());
             final T deltaEy     = osculating.getCircularEy().subtract(parameters[2].getValue());
             final T deltaI      = osculating.getI()         .subtract(parameters[3].getValue());
             final T deltaRAAN   = MathUtils.normalizeAngle(osculating.getRightAscensionOfAscendingNode().subtract(
                                                                 parameters[4].getValue()),
                                                                 zero);
             final T deltaAlphaM = MathUtils.normalizeAngle(osculating.getAlphaM().subtract(parameters[5].getValue()), zero);
             // update mean parameters
             current = new FieldEHModel<>(new FieldCircularOrbit<>(current.mean.getA().add(deltaA),
                                                                   current.mean.getCircularEx().add( deltaEx),
                                                                   current.mean.getCircularEy().add( deltaEy),
                                                                   current.mean.getI()         .add( deltaI ),
                                                                   current.mean.getRightAscensionOfAscendingNode().add(deltaRAAN),
                                                                   current.mean.getAlphaM().add(deltaAlphaM),
                                                                   PositionAngle.MEAN,
                                                                   current.mean.getFrame(),
                                                                   current.mean.getDate(), mu),
                                   mass, referenceRadius, mu, ck0);
             // check convergence
             if (FastMath.abs(deltaA.getReal())      < thresholdA.getReal() &&
                 FastMath.abs(deltaEx.getReal())     < thresholdE.getReal() &&
                 FastMath.abs(deltaEy.getReal())     < thresholdE.getReal() &&
                 FastMath.abs(deltaI.getReal())      < thresholdAngles.getReal() &&
                 FastMath.abs(deltaRAAN.getReal())   < thresholdAngles.getReal() &&
                 FastMath.abs(deltaAlphaM.getReal()) < thresholdAngles.getReal()) {
                 return current;
             }
 
         }
 
         throw new OrekitException(OrekitMessages.UNABLE_TO_COMPUTE_ECKSTEIN_HECHLER_MEAN_PARAMETERS, i);
 
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldCartesianOrbit<T> propagateOrbit(final FieldAbsoluteDate<T> date, final T[] parameters) {
         // compute Cartesian parameters, taking derivatives into account
         // to make sure velocity and acceleration are consistent
         final FieldEHModel<T> current = models.get(date);
         return new FieldCartesianOrbit<>(toCartesian(date, current.propagateParameters(date)),
                                          current.mean.getFrame(), mu);
     }
 
     /** Local class for Eckstein-Hechler model, with fixed mean parameters. */
     private static class FieldEHModel<T extends CalculusFieldElement<T>> {
 
         /** Mean FieldOrbit. */
         private final FieldCircularOrbit<T> mean;
 
         /** Constant mass. */
         private final T mass;
         // CHECKSTYLE: stop JavadocVariable check
 
         // preprocessed values
         private final T xnotDot;
         private final T rdpom;
         private final T rdpomp;
         private final T eps1;
         private final T eps2;
         private final T xim;
         private final T ommD;
         private final T rdl;
         private final T aMD;
 
         private final T kh;
         private final T kl;
 
         private final T ax1;
         private final T ay1;
         private final T as1;
         private final T ac2;
         private final T axy3;
         private final T as3;
         private final T ac4;
         private final T as5;
         private final T ac6;
 
         private final T ex1;
         private final T exx2;
         private final T exy2;
         private final T ex3;
         private final T ex4;
 
         private final T ey1;
         private final T eyx2;
         private final T eyy2;
         private final T ey3;
         private final T ey4;
 
         private final T rx1;
         private final T ry1;
         private final T r2;
         private final T r3;
         private final T rl;
 
         private final T iy1;
         private final T ix1;
         private final T i2;
         private final T i3;
         private final T ih;
 
         private final T lx1;
         private final T ly1;
         private final T l2;
         private final T l3;
         private final T ll;
 
         // CHECKSTYLE: resume JavadocVariable check
 
         /** Create a model for specified mean FieldOrbit.
          * @param mean mean FieldOrbit
          * @param mass constant mass
          * @param referenceRadius reference radius of the central body attraction model (m)
          * @param mu central attraction coefficient (m³/s²)
          * @param ck0 un-normalized zonal coefficients
          */
         FieldEHModel(final FieldCircularOrbit<T> mean, final T mass,
                      final double referenceRadius, final T mu, final double[] ck0) {
 
             this.mean            = mean;
             this.mass            = mass;
             final T zero = mass.getField().getZero();
             final T one  = mass.getField().getOne();
             // preliminary processing
             T q =  zero.add(referenceRadius).divide(mean.getA());
             T ql = q.multiply(q);
             final T g2 = ql.multiply(ck0[2]);
             ql = ql.multiply(q);
             final T g3 = ql.multiply(ck0[3]);
             ql = ql.multiply(q);
             final T g4 = ql.multiply(ck0[4]);
             ql = ql.multiply(q);
             final T g5 = ql.multiply(ck0[5]);
             ql = ql.multiply(q);
             final T g6 = ql.multiply(ck0[6]);
 
             final FieldSinCos<T> sc = FastMath.sinCos(mean.getI());
             final T cosI1 = sc.cos();
             final T sinI1 = sc.sin();
             final T sinI2 = sinI1.multiply(sinI1);
             final T sinI4 = sinI2.multiply(sinI2);
             final T sinI6 = sinI2.multiply(sinI4);
 
             if (sinI2.getReal() < 1.0e-10) {
                 throw new OrekitException(OrekitMessages.ALMOST_EQUATORIAL_ORBIT,
                                                FastMath.toDegrees(mean.getI().getReal()));
             }
 
             if (FastMath.abs(sinI2.getReal() - 4.0 / 5.0) < 1.0e-3) {
                 throw new OrekitException(OrekitMessages.ALMOST_CRITICALLY_INCLINED_ORBIT,
                                                FastMath.toDegrees(mean.getI().getReal()));
             }
 
             if (mean.getE().getReal() > 0.1) {
                 // if 0.005 < e < 0.1 no error is triggered, but accuracy is poor
                 throw new OrekitException(OrekitMessages.TOO_LARGE_ECCENTRICITY_FOR_PROPAGATION_MODEL,
                                                mean.getE());
             }
 
             xnotDot = mu.divide(mean.getA()).sqrt().divide(mean.getA());
 
             rdpom = g2.multiply(-0.75).multiply(sinI2.multiply(-5.0).add(4.0));
             rdpomp = g4.multiply(7.5).multiply(sinI2.multiply(-31.0 / 8.0).add(1.0).add( sinI4.multiply(49.0 / 16.0))).subtract(
                     g6.multiply(13.125).multiply(one.subtract(sinI2.multiply(8.0)).add(sinI4.multiply(129.0 / 8.0)).subtract(sinI6.multiply(297.0 / 32.0)) ));
 
 
             q = zero.add(3.0).divide(rdpom.multiply(32.0));
             eps1 = q.multiply(g4).multiply(sinI2).multiply(sinI2.multiply(-35.0).add(30.0)).subtract(
                    q.multiply(175.0).multiply(g6).multiply(sinI2).multiply(sinI2.multiply(-3.0).add(sinI4.multiply(2.0625)).add(1.0)));
             q = sinI1.multiply(3.0).divide(rdpom.multiply(8.0));
             eps2 = q.multiply(g3).multiply(sinI2.multiply(-5.0).add(4.0)).subtract(q.multiply(g5).multiply(sinI2.multiply(-35.0).add(sinI4.multiply(26.25)).add(10.0)));
 
             xim = mean.getI();
             ommD = cosI1.multiply(g2.multiply(1.50).subtract(g2.multiply(2.25).multiply(g2).multiply(sinI2.multiply(-19.0 / 6.0).add(2.5))).add(
                             g4.multiply(0.9375).multiply(sinI2.multiply(7.0).subtract(4.0))).add(
                             g6.multiply(3.28125).multiply(sinI2.multiply(-9.0).add(2.0).add(sinI4.multiply(8.25)))));
 
             rdl = g2.multiply(-1.50).multiply(sinI2.multiply(-4.0).add(3.0)).add(1.0);
             aMD = rdl.add(
                     g2.multiply(2.25).multiply(g2.multiply(sinI2.multiply(-263.0 / 12.0 ).add(9.0).add(sinI4.multiply(341.0 / 24.0))))).add(
                     g4.multiply(15.0 / 16.0).multiply(sinI2.multiply(-31.0).add(8.0).add(sinI4.multiply(24.5)))).add(
                     g6.multiply(105.0 / 32.0).multiply(sinI2.multiply(25.0).add(-10.0 / 3.0).subtract(sinI4.multiply(48.75)).add(sinI6.multiply(27.5))));
 
             final T qq   = g2.divide(rdl).multiply(-1.5);
             final T qA   = g2.multiply(0.75).multiply(g2).multiply(sinI2);
             final T qB   = g4.multiply(0.25).multiply(sinI2);
             final T qC   = g6.multiply(105.0 / 16.0).multiply(sinI2);
             final T qD   = g3.multiply(-0.75).multiply(sinI1);
             final T qE   = g5.multiply(3.75).multiply(sinI1);
             kh = zero.add(0.375).divide(rdpom);
             kl = kh.divide(sinI1);
 
             ax1 = qq.multiply(sinI2.multiply(-3.5).add(2.0));
             ay1 = qq.multiply(sinI2.multiply(-2.5).add(2.0));
             as1 = qD.multiply(sinI2.multiply(-5.0).add(4.0)).add(
                   qE.multiply(sinI4.multiply(2.625).add(sinI2.multiply(-3.5)).add(1.0)));
             ac2 = qq.multiply(sinI2).add(
                   qA.multiply(7.0).multiply(sinI2.multiply(-3.0).add(2.0))).add(
                   qB.multiply(sinI2.multiply(-17.5).add(15.0))).add(
                   qC.multiply(sinI2.multiply(3.0).subtract(1.0).subtract(sinI4.multiply(33.0 / 16.0))));
             axy3 = qq.multiply(3.5).multiply(sinI2);
             as3 = qD.multiply(5.0 / 3.0).multiply(sinI2).add(
                   qE.multiply(7.0 / 6.0).multiply(sinI2).multiply(sinI2.multiply(-1.125).add(1)));
             ac4 = qA.multiply(sinI2).add(
                   qB.multiply(4.375).multiply(sinI2)).add(
                   qC.multiply(0.75).multiply(sinI4.multiply(1.1).subtract(sinI2)));
 
             as5 = qE.multiply(21.0 / 80.0).multiply(sinI4);
 
             ac6 = qC.multiply(-11.0 / 80.0).multiply(sinI4);
 
             ex1 = qq.multiply(sinI2.multiply(-1.25).add(1.0));
             exx2 = qq.multiply(0.5).multiply(sinI2.multiply(-5.0).add(3.0));
             exy2 = qq.multiply(sinI2.multiply(-1.5).add(2.0));
             ex3 = qq.multiply(7.0 / 12.0).multiply(sinI2);
             ex4 = qq.multiply(17.0 / 8.0).multiply(sinI2);
 
             ey1 = qq.multiply(sinI2.multiply(-1.75).add(1.0));
             eyx2 = qq.multiply(sinI2.multiply(-3.0).add(1.0));
             eyy2 = qq.multiply(sinI2.multiply(2.0).subtract(1.5));
             ey3 = qq.multiply(7.0 / 12.0).multiply(sinI2);
             ey4 = qq.multiply(17.0 / 8.0).multiply(sinI2);
 
             q  = cosI1.multiply(qq).negate();
             rx1 = q.multiply(3.5);
             ry1 = q.multiply(-2.5);
             r2 = q.multiply(-0.5);
             r3 =  q.multiply(7.0 / 6.0);
             rl = g3 .multiply( cosI1).multiply(sinI2.multiply(-15.0).add(4.0)).subtract(
                  g5.multiply(2.5).multiply(cosI1).multiply(sinI2.multiply(-42.0).add(4.0).add(sinI4.multiply(52.5))));
 
             q = qq.multiply(0.5).multiply(sinI1).multiply(cosI1);
             iy1 =  q;
             ix1 = q.negate();
             i2 =  q;
             i3 =  q.multiply(7.0 / 3.0);
             ih = g3.negate().multiply(cosI1).multiply(sinI2.multiply(-5.0).add(4)).add(
                  g5.multiply(2.5).multiply(cosI1).multiply(sinI2.multiply(-14.0).add(4.0).add(sinI4.multiply(10.5))));
             lx1 = qq.multiply(sinI2.multiply(-77.0 / 8.0).add(7.0));
             ly1 = qq.multiply(sinI2.multiply(55.0 / 8.0).subtract(7.50));
             l2 = qq.multiply(sinI2.multiply(1.25).subtract(0.5));
             l3 = qq.multiply(sinI2.multiply(77.0 / 24.0).subtract(7.0 / 6.0));
             ll = g3.multiply(sinI2.multiply(53.0).subtract(4.0).add(sinI4.multiply(-57.5))).add(
                  g5.multiply(2.5).multiply(sinI2.multiply(-96.0).add(4.0).add(sinI4.multiply(269.5).subtract(sinI6.multiply(183.75)))));
 
         }
 
         /** Extrapolate a FieldOrbit up to a specific target date.
          * @param date target date for the FieldOrbit
          * @return propagated parameters
          */
         public FieldUnivariateDerivative2<T>[] propagateParameters(final FieldAbsoluteDate<T> date) {
             final Field<T> field = date.durationFrom(mean.getDate()).getField();
             final T one = field.getOne();
             final T zero = field.getZero();
             // Keplerian evolution
             final FieldUnivariateDerivative2<T> dt = new FieldUnivariateDerivative2<>(date.durationFrom(mean.getDate()), one, zero);
             final FieldUnivariateDerivative2<T> xnot = dt.multiply(xnotDot);
 
             // secular effects
 
             // eccentricity
             final FieldUnivariateDerivative2<T> x   = xnot.multiply(rdpom.add(rdpomp));
             final FieldUnivariateDerivative2<T> cx  = x.cos();
             final FieldUnivariateDerivative2<T> sx  = x.sin();
             final FieldUnivariateDerivative2<T> exm = cx.multiply(mean.getCircularEx()).
                                             add(sx.multiply(eps2.subtract(one.subtract(eps1).multiply(mean.getCircularEy()))));
             final FieldUnivariateDerivative2<T> eym = sx.multiply(eps1.add(1.0).multiply(mean.getCircularEx())).
                                             add(cx.multiply(mean.getCircularEy().subtract(eps2))).
                                             add(eps2);
             // no secular effect on inclination
 
             // right ascension of ascending node
             final FieldUnivariateDerivative2<T> omm =
                            new FieldUnivariateDerivative2<>(MathUtils.normalizeAngle(mean.getRightAscensionOfAscendingNode().add(ommD.multiply(xnot.getValue())),
                                                                                      one.getPi()),
                                                             ommD.multiply(xnotDot),
                                                             zero);
             // latitude argument
             final FieldUnivariateDerivative2<T> xlm =
                             new FieldUnivariateDerivative2<>(MathUtils.normalizeAngle(mean.getAlphaM().add(aMD.multiply(xnot.getValue())),
                                                                                       one.getPi()),
                                                            aMD.multiply(xnotDot),
                                                            zero);
 
             // periodical terms
             final FieldUnivariateDerivative2<T> cl1 = xlm.cos();
             final FieldUnivariateDerivative2<T> sl1 = xlm.sin();
             final FieldUnivariateDerivative2<T> cl2 = cl1.multiply(cl1).subtract(sl1.multiply(sl1));
             final FieldUnivariateDerivative2<T> sl2 = cl1.multiply(sl1).add(sl1.multiply(cl1));
             final FieldUnivariateDerivative2<T> cl3 = cl2.multiply(cl1).subtract(sl2.multiply(sl1));
             final FieldUnivariateDerivative2<T> sl3 = cl2.multiply(sl1).add(sl2.multiply(cl1));
             final FieldUnivariateDerivative2<T> cl4 = cl3.multiply(cl1).subtract(sl3.multiply(sl1));
             final FieldUnivariateDerivative2<T> sl4 = cl3.multiply(sl1).add(sl3.multiply(cl1));
             final FieldUnivariateDerivative2<T> cl5 = cl4.multiply(cl1).subtract(sl4.multiply(sl1));
             final FieldUnivariateDerivative2<T> sl5 = cl4.multiply(sl1).add(sl4.multiply(cl1));
             final FieldUnivariateDerivative2<T> cl6 = cl5.multiply(cl1).subtract(sl5.multiply(sl1));
 
             final FieldUnivariateDerivative2<T> qh  = eym.subtract(eps2).multiply(kh);
             final FieldUnivariateDerivative2<T> ql  = exm.multiply(kl);
 
             final FieldUnivariateDerivative2<T> exmCl1 = exm.multiply(cl1);
             final FieldUnivariateDerivative2<T> exmSl1 = exm.multiply(sl1);
             final FieldUnivariateDerivative2<T> eymCl1 = eym.multiply(cl1);
             final FieldUnivariateDerivative2<T> eymSl1 = eym.multiply(sl1);
             final FieldUnivariateDerivative2<T> exmCl2 = exm.multiply(cl2);
             final FieldUnivariateDerivative2<T> exmSl2 = exm.multiply(sl2);
             final FieldUnivariateDerivative2<T> eymCl2 = eym.multiply(cl2);
             final FieldUnivariateDerivative2<T> eymSl2 = eym.multiply(sl2);
             final FieldUnivariateDerivative2<T> exmCl3 = exm.multiply(cl3);
             final FieldUnivariateDerivative2<T> exmSl3 = exm.multiply(sl3);
             final FieldUnivariateDerivative2<T> eymCl3 = eym.multiply(cl3);
             final FieldUnivariateDerivative2<T> eymSl3 = eym.multiply(sl3);
             final FieldUnivariateDerivative2<T> exmCl4 = exm.multiply(cl4);
             final FieldUnivariateDerivative2<T> exmSl4 = exm.multiply(sl4);
             final FieldUnivariateDerivative2<T> eymCl4 = eym.multiply(cl4);
             final FieldUnivariateDerivative2<T> eymSl4 = eym.multiply(sl4);
 
             // semi major axis
             final FieldUnivariateDerivative2<T> rda = exmCl1.multiply(ax1).
                                             add(eymSl1.multiply(ay1)).
                                             add(sl1.multiply(as1)).
                                             add(cl2.multiply(ac2)).
                                             add(exmCl3.add(eymSl3).multiply(axy3)).
                                             add(sl3.multiply(as3)).
                                             add(cl4.multiply(ac4)).
                                             add(sl5.multiply(as5)).
                                             add(cl6.multiply(ac6));
 
             // eccentricity
             final FieldUnivariateDerivative2<T> rdex = cl1.multiply(ex1).
                                              add(exmCl2.multiply(exx2)).
                                              add(eymSl2.multiply(exy2)).
                                              add(cl3.multiply(ex3)).
                                              add(exmCl4.add(eymSl4).multiply(ex4));
             final FieldUnivariateDerivative2<T> rdey = sl1.multiply(ey1).
                                              add(exmSl2.multiply(eyx2)).
                                              add(eymCl2.multiply(eyy2)).
                                              add(sl3.multiply(ey3)).
                                              add(exmSl4.subtract(eymCl4).multiply(ey4));
 
             // ascending node
             final FieldUnivariateDerivative2<T> rdom = exmSl1.multiply(rx1).
                                              add(eymCl1.multiply(ry1)).
                                              add(sl2.multiply(r2)).
                                              add(eymCl3.subtract(exmSl3).multiply(r3)).
                                              add(ql.multiply(rl));
 
             // inclination
             final FieldUnivariateDerivative2<T> rdxi = eymSl1.multiply(iy1).
                                              add(exmCl1.multiply(ix1)).
                                              add(cl2.multiply(i2)).
                                              add(exmCl3.add(eymSl3).multiply(i3)).
                                              add(qh.multiply(ih));
 
             // latitude argument
             final FieldUnivariateDerivative2<T> rdxl = exmSl1.multiply(lx1).
                                              add(eymCl1.multiply(ly1)).
                                              add(sl2.multiply(l2)).
                                              add(exmSl3.subtract(eymCl3).multiply(l3)).
                                              add(ql.multiply(ll));
             // osculating parameters
             final FieldUnivariateDerivative2<T>[] FTD = MathArrays.buildArray(rdxl.getField(), 6);
 
             FTD[0] = rda.add(1.0).multiply(mean.getA());
             FTD[1] = rdex.add(exm);
             FTD[2] = rdey.add(eym);
             FTD[3] = rdxi.add(xim);
             FTD[4] = rdom.add(omm);
             FTD[5] = rdxl.add(xlm);
             return FTD;
 
         }
 
     }
 
     /** Convert circular parameters <em>with derivatives</em> to Cartesian coordinates.
      * @param date date of the parameters
      * @param parameters circular parameters (a, ex, ey, i, raan, alphaM)
      * @return Cartesian coordinates consistent with values and derivatives
      */
     private TimeStampedFieldPVCoordinates<T> toCartesian(final FieldAbsoluteDate<T> date, final FieldUnivariateDerivative2<T>[] parameters) {
 
         // evaluate coordinates in the FieldOrbit canonical reference frame
         final FieldUnivariateDerivative2<T> cosOmega = parameters[4].cos();
         final FieldUnivariateDerivative2<T> sinOmega = parameters[4].sin();
         final FieldUnivariateDerivative2<T> cosI     = parameters[3].cos();
         final FieldUnivariateDerivative2<T> sinI     = parameters[3].sin();
         final FieldUnivariateDerivative2<T> alphaE   = meanToEccentric(parameters[5], parameters[1], parameters[2]);
         final FieldUnivariateDerivative2<T> cosAE    = alphaE.cos();
         final FieldUnivariateDerivative2<T> sinAE    = alphaE.sin();
         final FieldUnivariateDerivative2<T> ex2      = parameters[1].multiply(parameters[1]);
         final FieldUnivariateDerivative2<T> ey2      = parameters[2].multiply(parameters[2]);
         final FieldUnivariateDerivative2<T> exy      = parameters[1].multiply(parameters[2]);
         final FieldUnivariateDerivative2<T> q        = ex2.add(ey2).subtract(1).negate().sqrt();
         final FieldUnivariateDerivative2<T> beta     = q.add(1).reciprocal();
         final FieldUnivariateDerivative2<T> bx2      = beta.multiply(ex2);
         final FieldUnivariateDerivative2<T> by2      = beta.multiply(ey2);
         final FieldUnivariateDerivative2<T> bxy      = beta.multiply(exy);
         final FieldUnivariateDerivative2<T> u        = bxy.multiply(sinAE).subtract(parameters[1].add(by2.subtract(1).multiply(cosAE)));
         final FieldUnivariateDerivative2<T> v        = bxy.multiply(cosAE).subtract(parameters[2].add(bx2.subtract(1).multiply(sinAE)));
         final FieldUnivariateDerivative2<T> x        = parameters[0].multiply(u);
         final FieldUnivariateDerivative2<T> y        = parameters[0].multiply(v);
 
         // canonical FieldOrbit reference frame
         final FieldVector3D<FieldUnivariateDerivative2<T>> p =
                 new FieldVector3D<>(x.multiply(cosOmega).subtract(y.multiply(cosI.multiply(sinOmega))),
                                     x.multiply(sinOmega).add(y.multiply(cosI.multiply(cosOmega))),
                                     y.multiply(sinI));
 
         // dispatch derivatives
         final FieldVector3D<T> p0 = new FieldVector3D<>(p.getX().getValue(),
                                                         p.getY().getValue(),
                                                         p.getZ().getValue());
         final FieldVector3D<T> p1 = new FieldVector3D<>(p.getX().getFirstDerivative(),
                                                         p.getY().getFirstDerivative(),
                                                         p.getZ().getFirstDerivative());
         final FieldVector3D<T> p2 = new FieldVector3D<>(p.getX().getSecondDerivative(),
                                                         p.getY().getSecondDerivative(),
                                                         p.getZ().getSecondDerivative());
         return new TimeStampedFieldPVCoordinates<>(date, p0, p1, p2);
 
     }
 
     /** Computes the eccentric latitude argument from the mean latitude argument.
      * @param alphaM = M + Ω mean latitude argument (rad)
      * @param ex e cos(Ω), first component of circular eccentricity vector
      * @param ey e sin(Ω), second component of circular eccentricity vector
      * @return the eccentric latitude argument.
      */
     private FieldUnivariateDerivative2<T> meanToEccentric(final FieldUnivariateDerivative2<T> alphaM,
                                                 final FieldUnivariateDerivative2<T> ex,
                                                 final FieldUnivariateDerivative2<T> ey) {
         // Generalization of Kepler equation to circular parameters
         // with alphaE = PA + E and
         //      alphaM = PA + M = alphaE - ex.sin(alphaE) + ey.cos(alphaE)
         FieldUnivariateDerivative2<T> alphaE        = alphaM;
         FieldUnivariateDerivative2<T> shift         = alphaM.getField().getZero();
         FieldUnivariateDerivative2<T> alphaEMalphaM = alphaM.getField().getZero();
         FieldUnivariateDerivative2<T> cosAlphaE     = alphaE.cos();
         FieldUnivariateDerivative2<T> sinAlphaE     = alphaE.sin();
         int                 iter          = 0;
         do {
             final FieldUnivariateDerivative2<T> f2 = ex.multiply(sinAlphaE).subtract(ey.multiply(cosAlphaE));
             final FieldUnivariateDerivative2<T> f1 = alphaM.getField().getOne().subtract(ex.multiply(cosAlphaE)).subtract(ey.multiply(sinAlphaE));
             final FieldUnivariateDerivative2<T> f0 = alphaEMalphaM.subtract(f2);
 
             final FieldUnivariateDerivative2<T> f12 = f1.multiply(2);
             shift = f0.multiply(f12).divide(f1.multiply(f12).subtract(f0.multiply(f2)));
 
             alphaEMalphaM  = alphaEMalphaM.subtract(shift);
             alphaE         = alphaM.add(alphaEMalphaM);
             cosAlphaE      = alphaE.cos();
             sinAlphaE      = alphaE.sin();
 
         } while (++iter < 50 && FastMath.abs(shift.getValue().getReal()) > 1.0e-12);
 
         return alphaE;
 
     }
 
     /** {@inheritDoc} */
     @Override
     protected T getMass(final FieldAbsoluteDate<T> date) {
         return models.get(date).mass;
     }
 
     /** {@inheritDoc} */
     @Override
     protected List<ParameterDriver> getParametersDrivers() {
         // Eckstein Hechler propagation model does not have parameter drivers.
         return Collections.emptyList();
     }
 
 }