/* Copyright 2002-2024 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.integration;
  
  import java.util.ArrayList;
  import java.util.Arrays;
  import java.util.Collection;
  import java.util.Collections;
  import java.util.HashMap;
  import java.util.LinkedList;
  import java.util.List;
  import java.util.Map;
  import java.util.Queue;
  
  import org.hipparchus.analysis.UnivariateFunction;
  import org.hipparchus.analysis.solvers.BracketedUnivariateSolver;
  import org.hipparchus.analysis.solvers.BracketingNthOrderBrentSolver;
  import org.hipparchus.exception.MathRuntimeException;
  import org.hipparchus.ode.DenseOutputModel;
  import org.hipparchus.ode.ExpandableODE;
  import org.hipparchus.ode.ODEIntegrator;
  import org.hipparchus.ode.ODEState;
  import org.hipparchus.ode.ODEStateAndDerivative;
  import org.hipparchus.ode.OrdinaryDifferentialEquation;
  import org.hipparchus.ode.SecondaryODE;
  import org.hipparchus.ode.events.Action;
  import org.hipparchus.ode.events.AdaptableInterval;
  import org.hipparchus.ode.events.ODEEventDetector;
  import org.hipparchus.ode.events.ODEEventHandler;
  import org.hipparchus.ode.sampling.AbstractODEStateInterpolator;
  import org.hipparchus.ode.sampling.ODEStateInterpolator;
  import org.hipparchus.ode.sampling.ODEStepHandler;
  import org.hipparchus.util.Precision;
  import org.orekit.attitudes.AttitudeProvider;
  import org.orekit.errors.OrekitException;
  import org.orekit.errors.OrekitInternalError;
  import org.orekit.errors.OrekitMessages;
  import org.orekit.frames.Frame;
  import org.orekit.orbits.OrbitType;
  import org.orekit.orbits.PositionAngleType;
  import org.orekit.propagation.AbstractPropagator;
  import org.orekit.propagation.BoundedPropagator;
  import org.orekit.propagation.EphemerisGenerator;
  import org.orekit.propagation.PropagationType;
  import org.orekit.propagation.SpacecraftState;
  import org.orekit.propagation.events.EventDetector;
  import org.orekit.propagation.events.handlers.EventHandler;
  import org.orekit.propagation.sampling.OrekitStepHandler;
  import org.orekit.propagation.sampling.OrekitStepInterpolator;
  import org.orekit.time.AbsoluteDate;
  import org.orekit.utils.DoubleArrayDictionary;
  
  
  /** Common handling of {@link org.orekit.propagation.Propagator Propagator}
   *  methods for both numerical and semi-analytical propagators.
   *  @author Luc Maisonobe
   */
  public abstract class AbstractIntegratedPropagator extends AbstractPropagator {
  
      /** Internal name used for complete secondary state dimension.
       * @since 11.1
       */
      private static final String SECONDARY_DIMENSION = "Orekit-secondary-dimension";
  
      /** Event detectors not related to force models. */
      private final List<EventDetector> detectors;
  
      /** Step handlers dedicated to ephemeris generation. */
      private final List<StoringStepHandler> ephemerisGenerators;
  
      /** Integrator selected by the user for the orbital extrapolation process. */
      private final ODEIntegrator integrator;
  
      /** Offsets of secondary states managed by {@link AdditionalDerivativesProvider}.
       * @since 11.1
       */
      private final Map<String, Integer> secondaryOffsets;
  
      /** Additional derivatives providers.
       * @since 11.1
       */
      private final List<AdditionalDerivativesProvider> additionalDerivativesProviders;
  
      /** Map of secondary equation offset in main
      /** Counter for differential equations calls. */
     private int calls;
 
     /** Mapper between raw double components and space flight dynamics objects. */
     private StateMapper stateMapper;
 
     /**
      * Attitude provider when evaluating derivatives. Can be a frozen one for performance.
      * @since 12.1
      */
     private AttitudeProvider attitudeProviderForDerivatives;
 
     /** Flag for resetting the state at end of propagation. */
     private boolean resetAtEnd;
 
     /** Type of orbit to output (mean or osculating) <br/>
      * <p>
      * This is used only in the case of semi-analytical propagators where there is a clear separation between
      * mean and short periodic elements. It is ignored by the Numerical propagator.
      * </p>
      */
     private final PropagationType propagationType;
 
     /** Build a new instance.
      * @param integrator numerical integrator to use for propagation.
      * @param propagationType type of orbit to output (mean or osculating).
      */
     protected AbstractIntegratedPropagator(final ODEIntegrator integrator, final PropagationType propagationType) {
         detectors                      = new ArrayList<>();
         ephemerisGenerators            = new ArrayList<>();
         additionalDerivativesProviders = new ArrayList<>();
         this.secondaryOffsets          = new HashMap<>();
         this.integrator                = integrator;
         this.propagationType           = propagationType;
         this.resetAtEnd                = true;
     }
 
     /** Allow/disallow resetting the initial state at end of propagation.
      * <p>
      * By default, at the end of the propagation, the propagator resets the initial state
      * to the final state, thus allowing a new propagation to be started from there without
      * recomputing the part already performed. Calling this method with {@code resetAtEnd} set
      * to false changes prevents such reset.
      * </p>
      * @param resetAtEnd if true, at end of each propagation, the {@link
      * #getInitialState() initial state} will be reset to the final state of
      * the propagation, otherwise the initial state will be preserved
      * @since 9.0
      */
     public void setResetAtEnd(final boolean resetAtEnd) {
         this.resetAtEnd = resetAtEnd;
     }
 
     /** Getter for the resetting flag regarding initial state.
      * @return resetting flag
      * @since 12.0
      */
     public boolean getResetAtEnd() {
         return this.resetAtEnd;
     }
 
     /**
      * Method called when initializing the attitude provider used when evaluating derivatives.
      * @return attitude provider for derivatives
      */
     protected AttitudeProvider initializeAttitudeProviderForDerivatives() {
         return getAttitudeProvider();
     }
 
     /** Initialize the mapper. */
     protected void initMapper() {
         stateMapper = createMapper(null, Double.NaN, null, null, null, null);
     }
 
     /** Get the integrator's name.
      * @return name of underlying integrator
      * @since 12.0
      */
     public String getIntegratorName() {
         return integrator.getName();
     }
 
     /**  {@inheritDoc} */
     @Override
     public void setAttitudeProvider(final AttitudeProvider attitudeProvider) {
         super.setAttitudeProvider(attitudeProvider);
         stateMapper = createMapper(stateMapper.getReferenceDate(), stateMapper.getMu(),
                                    stateMapper.getOrbitType(), stateMapper.getPositionAngleType(),
                                    attitudeProvider, stateMapper.getFrame());
     }
 
     /** Set propagation orbit type.
      * @param orbitType orbit type to use for propagation, null for
      * propagating using {@link org.orekit.utils.AbsolutePVCoordinates AbsolutePVCoordinates}
      * rather than {@link org.orekit.orbits Orbit}
      */
     protected void setOrbitType(final OrbitType orbitType) {
         stateMapper = createMapper(stateMapper.getReferenceDate(), stateMapper.getMu(),
                                    orbitType, stateMapper.getPositionAngleType(),
                                    stateMapper.getAttitudeProvider(), stateMapper.getFrame());
     }
 
     /** Get propagation parameter type.
      * @return orbit type used for propagation, null for
      * propagating using {@link org.orekit.utils.AbsolutePVCoordinates AbsolutePVCoordinates}
      * rather than {@link org.orekit.orbits Orbit}
      */
     protected OrbitType getOrbitType() {
         return stateMapper.getOrbitType();
     }
 
     /** Get the propagation type.
      * @return propagation type.
      * @since 11.1
      */
     public PropagationType getPropagationType() {
         return propagationType;
     }
 
     /** Set position angle type.
      * <p>
      * The position parameter type is meaningful only if {@link
      * #getOrbitType() propagation orbit type}
      * support it. As an example, it is not meaningful for propagation
      * in {@link OrbitType#CARTESIAN Cartesian} parameters.
      * </p>
      * @param positionAngleType angle type to use for propagation
      */
     protected void setPositionAngleType(final PositionAngleType positionAngleType) {
         stateMapper = createMapper(stateMapper.getReferenceDate(), stateMapper.getMu(),
                                    stateMapper.getOrbitType(), positionAngleType,
                                    stateMapper.getAttitudeProvider(), stateMapper.getFrame());
     }
 
     /** Get propagation parameter type.
      * @return angle type to use for propagation
      */
     protected PositionAngleType getPositionAngleType() {
         return stateMapper.getPositionAngleType();
     }
 
     /** Set the central attraction coefficient μ.
      * @param mu central attraction coefficient (m³/s²)
      */
     public void setMu(final double mu) {
         stateMapper = createMapper(stateMapper.getReferenceDate(), mu,
                                    stateMapper.getOrbitType(), stateMapper.getPositionAngleType(),
                                    stateMapper.getAttitudeProvider(), stateMapper.getFrame());
     }
 
     /** Get the central attraction coefficient μ.
      * @return mu central attraction coefficient (m³/s²)
      * @see #setMu(double)
      */
     public double getMu() {
         return stateMapper.getMu();
     }
 
     /** Get the number of calls to the differential equations computation method.
      * <p>The number of calls is reset each time the {@link #propagate(AbsoluteDate)}
      * method is called.</p>
      * @return number of calls to the differential equations computation method
      */
     public int getCalls() {
         return calls;
     }
 
     /** {@inheritDoc} */
     @Override
     public boolean isAdditionalStateManaged(final String name) {
 
         // first look at already integrated states
         if (super.isAdditionalStateManaged(name)) {
             return true;
         }
 
         // then look at states we integrate ourselves
         for (final AdditionalDerivativesProvider provider : additionalDerivativesProviders) {
             if (provider.getName().equals(name)) {
                 return true;
             }
         }
 
         return false;
     }
 
     /** {@inheritDoc} */
     @Override
     public String[] getManagedAdditionalStates() {
         final String[] alreadyIntegrated = super.getManagedAdditionalStates();
         final String[] managed = new String[alreadyIntegrated.length + additionalDerivativesProviders.size()];
         System.arraycopy(alreadyIntegrated, 0, managed, 0, alreadyIntegrated.length);
         for (int i = 0; i < additionalDerivativesProviders.size(); ++i) {
             managed[i + alreadyIntegrated.length] = additionalDerivativesProviders.get(i).getName();
         }
         return managed;
     }
 
     /** Add a provider for user-specified state derivatives to be integrated along with the orbit propagation.
      * @param provider provider for additional derivatives
      * @see #addAdditionalStateProvider(org.orekit.propagation.AdditionalStateProvider)
      * @since 11.1
      */
     public void addAdditionalDerivativesProvider(final AdditionalDerivativesProvider provider) {
 
         // check if the name is already used
         if (isAdditionalStateManaged(provider.getName())) {
             // these derivatives are already registered, complain
             throw new OrekitException(OrekitMessages.ADDITIONAL_STATE_NAME_ALREADY_IN_USE,
                                       provider.getName());
         }
 
         // this is really a new set of derivatives, add it
         additionalDerivativesProviders.add(provider);
 
         secondaryOffsets.clear();
 
     }
 
     /** Get an unmodifiable list of providers for additional derivatives.
      * @return providers for the additional derivatives
      * @since 11.1
      */
     public List<AdditionalDerivativesProvider> getAdditionalDerivativesProviders() {
         return Collections.unmodifiableList(additionalDerivativesProviders);
     }
 
     /** {@inheritDoc} */
     public void addEventDetector(final EventDetector detector) {
         detectors.add(detector);
     }
 
     /** {@inheritDoc} */
     public Collection<EventDetector> getEventsDetectors() {
         return Collections.unmodifiableCollection(detectors);
     }
 
     /** {@inheritDoc} */
     public void clearEventsDetectors() {
         detectors.clear();
     }
 
     /** Set up all user defined event detectors.
      */
     protected void setUpUserEventDetectors() {
         for (final EventDetector detector : detectors) {
             setUpEventDetector(integrator, detector);
         }
     }
 
     /** Wrap an Orekit event detector and register it to the integrator.
      * @param integ integrator into which event detector should be registered
      * @param detector event detector to wrap
      */
     protected void setUpEventDetector(final ODEIntegrator integ, final EventDetector detector) {
         integ.addEventDetector(new AdaptedEventDetector(detector));
     }
 
     /** {@inheritDoc} */
     @Override
     public EphemerisGenerator getEphemerisGenerator() {
         final StoringStepHandler storingHandler = new StoringStepHandler();
         ephemerisGenerators.add(storingHandler);
         return storingHandler;
     }
 
     /** Create a mapper between raw double components and spacecraft state.
     /** Simple constructor.
      * <p>
      * The position parameter type is meaningful only if {@link
      * #getOrbitType() propagation orbit type}
      * support it. As an example, it is not meaningful for propagation
      * in {@link OrbitType#CARTESIAN Cartesian} parameters.
      * </p>
      * @param referenceDate reference date
      * @param mu central attraction coefficient (m³/s²)
      * @param orbitType orbit type to use for mapping
      * @param positionAngleType angle type to use for propagation
      * @param attitudeProvider attitude provider
      * @param frame inertial frame
      * @return new mapper
      */
     protected abstract StateMapper createMapper(AbsoluteDate referenceDate, double mu,
                                                 OrbitType orbitType, PositionAngleType positionAngleType,
                                                 AttitudeProvider attitudeProvider, Frame frame);
 
     /** Get the differential equations to integrate (for main state only).
      * @param integ numerical integrator to use for propagation.
      * @return differential equations for main state
      */
     protected abstract MainStateEquations getMainStateEquations(ODEIntegrator integ);
 
     /** {@inheritDoc} */
     @Override
     public SpacecraftState propagate(final AbsoluteDate target) {
         if (getStartDate() == null) {
             if (getInitialState() == null) {
                 throw new OrekitException(OrekitMessages.INITIAL_STATE_NOT_SPECIFIED_FOR_ORBIT_PROPAGATION);
             }
             setStartDate(getInitialState().getDate());
         }
         return propagate(getStartDate(), target);
     }
 
     /** {@inheritDoc} */
     public SpacecraftState propagate(final AbsoluteDate tStart, final AbsoluteDate tEnd) {
 
         if (getInitialState() == null) {
             throw new OrekitException(OrekitMessages.INITIAL_STATE_NOT_SPECIFIED_FOR_ORBIT_PROPAGATION);
         }
 
         // make sure the integrator will be reset properly even if we change its events handlers and step handlers
         try (IntegratorResetter resetter = new IntegratorResetter(integrator)) {
 
             // prepare handling of STM and Jacobian matrices
             setUpStmAndJacobianGenerators();
 
             // Initialize additional states
             initializeAdditionalStates(tEnd);
 
             if (!tStart.equals(getInitialState().getDate())) {
                 // if propagation start date is not initial date,
                 // propagate from initial to start date without event detection
                 try (IntegratorResetter startResetter = new IntegratorResetter(integrator)) {
                     integrateDynamics(tStart, true);
                 }
             }
 
             // set up events added by user
             setUpUserEventDetectors();
 
             // set up step handlers
             for (final OrekitStepHandler handler : getMultiplexer().getHandlers()) {
                 integrator.addStepHandler(new AdaptedStepHandler(handler));
             }
             for (final StoringStepHandler generator : ephemerisGenerators) {
                 generator.setEndDate(tEnd);
                 integrator.addStepHandler(generator);
             }
 
             // propagate from start date to end date with event detection
             final SpacecraftState finalState = integrateDynamics(tEnd, false);
 
             return finalState;
 
         }
 
     }
 
     /** Set up State Transition Matrix and Jacobian matrix handling.
      * @since 11.1
      */
     protected void setUpStmAndJacobianGenerators() {
         // nothing to do by default
     }
 
     /** Propagation with or without event detection.
      * @param tEnd target date to which orbit should be propagated
      * @param forceResetAtEnd flag to force resetting state and date after integration
      * @return state at end of propagation
      */
     private SpacecraftState integrateDynamics(final AbsoluteDate tEnd, final boolean forceResetAtEnd) {
         try {
 
             initializePropagation();
 
             if (getInitialState().getDate().equals(tEnd)) {
                 // don't extrapolate
                 return getInitialState();
             }
 
             // space dynamics view
             stateMapper = createMapper(getInitialState().getDate(), stateMapper.getMu(),
                                        stateMapper.getOrbitType(), stateMapper.getPositionAngleType(),
                                        stateMapper.getAttitudeProvider(), getInitialState().getFrame());
             attitudeProviderForDerivatives = initializeAttitudeProviderForDerivatives();
 
             if (Double.isNaN(getMu())) {
                 setMu(getInitialState().getMu());
             }
 
             if (getInitialState().getMass() <= 0.0) {
                 throw new OrekitException(OrekitMessages.NOT_POSITIVE_SPACECRAFT_MASS,
                                           getInitialState().getMass());
             }
 
             // convert space flight dynamics API to math API
             final SpacecraftState initialIntegrationState = getInitialIntegrationState();
             final ODEState mathInitialState = createInitialState(initialIntegrationState);
             final ExpandableODE mathODE = createODE(integrator);
 
             // mathematical integration
             final ODEStateAndDerivative mathFinalState;
             beforeIntegration(initialIntegrationState, tEnd);
             mathFinalState = integrator.integrate(mathODE, mathInitialState,
                                                   tEnd.durationFrom(getInitialState().getDate()));
             afterIntegration();
 
             // get final state
             SpacecraftState finalState =
                             stateMapper.mapArrayToState(stateMapper.mapDoubleToDate(mathFinalState.getTime(),
                                                                                     tEnd),
                                                         mathFinalState.getPrimaryState(),
                                                         mathFinalState.getPrimaryDerivative(),
                                                         propagationType);
 
             finalState = updateAdditionalStatesAndDerivatives(finalState, mathFinalState);
 
             if (resetAtEnd || forceResetAtEnd) {
                 resetInitialState(finalState);
                 setStartDate(finalState.getDate());
             }
 
             return finalState;
 
         } catch (MathRuntimeException mre) {
             throw OrekitException.unwrap(mre);
         }
     }
 
     /**
      * Returns an updated version of the inputted state with additional states, including
      * from derivatives providers.
      * @param originalState input state
      * @param os ODE state and derivative
      * @return new state
      * @since 12.1
      */
     private SpacecraftState updateAdditionalStatesAndDerivatives(final SpacecraftState originalState,
                                                                  final ODEStateAndDerivative os) {
         SpacecraftState updatedState = originalState;
         if (os.getNumberOfSecondaryStates() > 0) {
             final double[] secondary           = os.getSecondaryState(1);
             final double[] secondaryDerivative = os.getSecondaryDerivative(1);
             for (final AdditionalDerivativesProvider provider : additionalDerivativesProviders) {
                 final String name      = provider.getName();
                 final int    offset    = secondaryOffsets.get(name);
                 final int    dimension = provider.getDimension();
                 updatedState = updatedState.addAdditionalState(name, Arrays.copyOfRange(secondary, offset, offset + dimension));
                 updatedState = updatedState.addAdditionalStateDerivative(name, Arrays.copyOfRange(secondaryDerivative, offset, offset + dimension));
             }
         }
         return updateAdditionalStates(updatedState);
     }
 
     /** Get the initial state for integration.
      * @return initial state for integration
      */
     protected SpacecraftState getInitialIntegrationState() {
         return getInitialState();
     }
 
     /** Create an initial state.
      * @param initialState initial state in flight dynamics world
      * @return initial state in mathematics world
      */
     private ODEState createInitialState(final SpacecraftState initialState) {
 
         // retrieve initial state
         final double[] primary = new double[getBasicDimension()];
         stateMapper.mapStateToArray(initialState, primary, null);
 
         if (secondaryOffsets.isEmpty()) {
             // compute dimension of the secondary state
             int offset = 0;
             for (final AdditionalDerivativesProvider provider : additionalDerivativesProviders) {
                 secondaryOffsets.put(provider.getName(), offset);
                 offset += provider.getDimension();
             }
             secondaryOffsets.put(SECONDARY_DIMENSION, offset);
         }
 
         return new ODEState(0.0, primary, secondary(initialState));
 
     }
 
     /** Create secondary state.
      * @param state spacecraft state
      * @return secondary state
      * @since 11.1
      */
     private double[][] secondary(final SpacecraftState state) {
 
         if (secondaryOffsets.isEmpty()) {
             return null;
         }
 
         final double[][] secondary = new double[1][secondaryOffsets.get(SECONDARY_DIMENSION)];
         for (final AdditionalDerivativesProvider provider : additionalDerivativesProviders) {
             final String   name       = provider.getName();
             final int      offset     = secondaryOffsets.get(name);
             final double[] additional = state.getAdditionalState(name);
             System.arraycopy(additional, 0, secondary[0], offset, additional.length);
         }
 
         return secondary;
 
     }
 
     /** Create secondary state derivative.
      * @param state spacecraft state
      * @return secondary state derivative
      * @since 11.1
      */
     private double[][] secondaryDerivative(final SpacecraftState state) {
 
         if (secondaryOffsets.isEmpty()) {
             return null;
         }
 
         final double[][] secondaryDerivative = new double[1][secondaryOffsets.get(SECONDARY_DIMENSION)];
         for (final AdditionalDerivativesProvider provider : additionalDerivativesProviders) {
             final String   name       = provider.getName();
             final int      offset     = secondaryOffsets.get(name);
             final double[] additionalDerivative = state.getAdditionalStateDerivative(name);
             System.arraycopy(additionalDerivative, 0, secondaryDerivative[0], offset, additionalDerivative.length);
         }
 
         return secondaryDerivative;
 
     }
 
     /** Create an ODE with all equations.
      * @param integ numerical integrator to use for propagation.
      * @return a new ode
      */
     private ExpandableODE createODE(final ODEIntegrator integ) {
 
         final ExpandableODE ode =
                 new ExpandableODE(new ConvertedMainStateEquations(getMainStateEquations(integ)));
 
         // secondary part of the ODE
         if (!additionalDerivativesProviders.isEmpty()) {
             ode.addSecondaryEquations(new ConvertedSecondaryStateEquations());
         }
 
         return ode;
 
     }
 
     /** Method called just before integration.
      * <p>
      * The default implementation does nothing, it may be specialized in subclasses.
      * </p>
      * @param initialState initial state
      * @param tEnd target date at which state should be propagated
      */
     protected void beforeIntegration(final SpacecraftState initialState,
                                      final AbsoluteDate tEnd) {
         // do nothing by default
     }
 
     /** Method called just after integration.
      * <p>
      * The default implementation does nothing, it may be specialized in subclasses.
      * </p>
      */
     protected void afterIntegration() {
         // do nothing by default
     }
 
     /** Get state vector dimension without additional parameters.
      * @return state vector dimension without additional parameters.
      */
     public int getBasicDimension() {
         return 7;
     }
 
     /** Get the integrator used by the propagator.
      * @return the integrator.
      */
     protected ODEIntegrator getIntegrator() {
         return integrator;
     }
 
     /** Convert a state from mathematical world to space flight dynamics world.
      * @param os mathematical state
      * @return space flight dynamics state
      */
     private SpacecraftState convert(final ODEStateAndDerivative os) {
 
         final SpacecraftState s = stateMapper.mapArrayToState(os.getTime(), os.getPrimaryState(),
             os.getPrimaryDerivative(), propagationType);
         return updateAdditionalStatesAndDerivatives(s, os);
     }
 
     /** Convert a state from space flight dynamics world to mathematical world.
      * @param state space flight dynamics state
      * @return mathematical state
      */
     private ODEStateAndDerivative convert(final SpacecraftState state) {
 
         // retrieve initial state
         final double[] primary    = new double[getBasicDimension()];
         final double[] primaryDot = new double[getBasicDimension()];
         stateMapper.mapStateToArray(state, primary, primaryDot);
 
         // secondary part of the ODE
         final double[][] secondary           = secondary(state);
         final double[][] secondaryDerivative = secondaryDerivative(state);
 
         return new ODEStateAndDerivative(stateMapper.mapDateToDouble(state.getDate()),
                                          primary, primaryDot,
                                          secondary, secondaryDerivative);
 
     }
 
     /** Differential equations for the main state (orbit, attitude and mass). */
     public interface MainStateEquations {
 
         /**
          * Initialize the equations at the start of propagation. This method will be
          * called before any calls to {@link #computeDerivatives(SpacecraftState)}.
          *
          * <p> The default implementation of this method does nothing.
          *
          * @param initialState initial state information at the start of propagation.
          * @param target       date of propagation. Not equal to {@code
          *                     initialState.getDate()}.
          */
         default void init(final SpacecraftState initialState, final AbsoluteDate target) {
         }
 
         /** Compute differential equations for main state.
          * @param state current state
          * @return derivatives of main state
          */
         double[] computeDerivatives(SpacecraftState state);
 
     }
 
     /** Differential equations for the main state (orbit, attitude and mass), with converted API. */
     private class ConvertedMainStateEquations implements OrdinaryDifferentialEquation {
 
         /** Main state equations. */
         private final MainStateEquations main;
 
         /** Simple constructor.
          * @param main main state equations
          */
         ConvertedMainStateEquations(final MainStateEquations main) {
             this.main = main;
             calls = 0;
         }
 
         /** {@inheritDoc} */
         public int getDimension() {
             return getBasicDimension();
         }
 
         @Override
         public void init(final double t0, final double[] y0, final double finalTime) {
             // update space dynamics view
             SpacecraftState initialState = stateMapper.mapArrayToState(t0, y0, null, PropagationType.MEAN);
             initialState = updateAdditionalStates(initialState);
             initialState = updateStatesFromAdditionalDerivativesIfKnown(initialState);
             final AbsoluteDate target = stateMapper.mapDoubleToDate(finalTime);
             main.init(initialState, target);
             attitudeProviderForDerivatives = initializeAttitudeProviderForDerivatives();
         }
 
         /**
          * Returns an updated version of the inputted state, with additional states from
          * derivatives providers as given in the stored initial state.
          * @param originalState input state
          * @return new state
          * @since 12.1
          */
         private SpacecraftState updateStatesFromAdditionalDerivativesIfKnown(final SpacecraftState originalState) {
             SpacecraftState updatedState = originalState;
             final SpacecraftState storedInitialState = getInitialState();
             final double originalTime = stateMapper.mapDateToDouble(originalState.getDate());
             if (storedInitialState != null && stateMapper.mapDateToDouble(storedInitialState.getDate()) == originalTime) {
                 for (final AdditionalDerivativesProvider provider: additionalDerivativesProviders) {
                     final String name = provider.getName();
                     final double[] value = storedInitialState.getAdditionalState(name);
                     updatedState = updatedState.addAdditionalState(name, value);
                 }
             }
             return updatedState;
         }
 
         /** {@inheritDoc} */
         public double[] computeDerivatives(final double t, final double[] y) {
 
             // increment calls counter
             ++calls;
 
             // update space dynamics view
             stateMapper.setAttitudeProvider(attitudeProviderForDerivatives);
             SpacecraftState currentState = stateMapper.mapArrayToState(t, y, null, PropagationType.MEAN);
             stateMapper.setAttitudeProvider(getAttitudeProvider());
 
             currentState = updateAdditionalStates(currentState);
             // compute main state differentials
             return main.computeDerivatives(currentState);
 
         }
 
     }
 
     /** Differential equations for the secondary state (Jacobians, user variables ...), with converted API. */
     private class ConvertedSecondaryStateEquations implements SecondaryODE {
 
         /** Dimension of the combined additional states. */
         private final int combinedDimension;
 
         /** Simple constructor.
           */
         ConvertedSecondaryStateEquations() {
             this.combinedDimension = secondaryOffsets.get(SECONDARY_DIMENSION);
         }
 
         /** {@inheritDoc} */
         @Override
         public int getDimension() {
             return combinedDimension;
         }
 
         /** {@inheritDoc} */
         @Override
         public void init(final double t0, final double[] primary0,
                          final double[] secondary0, final double finalTime) {
             // update space dynamics view
             final SpacecraftState initialState = convert(t0, primary0, null, secondary0);
 
             final AbsoluteDate target = stateMapper.mapDoubleToDate(finalTime);
             for (final AdditionalDerivativesProvider provider : additionalDerivativesProviders) {
                 provider.init(initialState, target);
             }
 
         }
 
         /** {@inheritDoc} */
         @Override
         public double[] computeDerivatives(final double t, final double[] primary,
                                            final double[] primaryDot, final double[] secondary) {
 
             // update space dynamics view
             // the integrable generators generate method will be called here,
             // according to the generators yield order
             SpacecraftState updated = convert(t, primary, primaryDot, secondary);
 
             // set up queue for equations
             final Queue<AdditionalDerivativesProvider> pending = new LinkedList<>(additionalDerivativesProviders);
 
             // gather the derivatives from all additional equations, taking care of dependencies
             final double[] secondaryDot = new double[combinedDimension];
             int yieldCount = 0;
             while (!pending.isEmpty()) {
                 final AdditionalDerivativesProvider provider = pending.remove();
                 if (provider.yields(updated)) {
                     // this provider has to wait for another one,
                     // we put it again in the pending queue
                     pending.add(provider);
                     if (++yieldCount >= pending.size()) {
                         // all pending providers yielded!, they probably need data not yet initialized
                         // we let the propagation proceed, if these data are really needed right now
                         // an appropriate exception will be triggered when caller tries to access them
                         break;
                     }
                 } else {
                     // we can use these equations right now
                     final String              name           = provider.getName();
                     final int                 offset         = secondaryOffsets.get(name);
                     final int                 dimension      = provider.getDimension();
                     final CombinedDerivatives derivatives    = provider.combinedDerivatives(updated);
                     final double[]            additionalPart = derivatives.getAdditionalDerivatives();
                     final double[]            mainPart       = derivatives.getMainStateDerivativesIncrements();
                     System.arraycopy(additionalPart, 0, secondaryDot, offset, dimension);
                     updated = updated.addAdditionalStateDerivative(name, additionalPart);
                     if (mainPart != null) {
                         // this equation does change the main state derivatives
                         for (int i = 0; i < mainPart.length; ++i) {
                             primaryDot[i] += mainPart[i];
                         }
                     }
                     yieldCount = 0;
                 }
             }
 
             return secondaryDot;
 
         }
 
         /** Convert mathematical view to space view.
          * @param t current value of the independent <I>time</I> variable
          * @param primary array containing the current value of the primary state vector
          * @param primaryDot array containing the derivative of the primary state vector
          * @param secondary array containing the current value of the secondary state vector
          * @return space view of the state
          */
         private SpacecraftState convert(final double t, final double[] primary,
                                         final double[] primaryDot, final double[] secondary) {
 
             SpacecraftState initialState = stateMapper.mapArrayToState(t, primary, primaryDot, PropagationType.MEAN);
 
             for (final AdditionalDerivativesProvider provider : additionalDerivativesProviders) {
                 final String name      = provider.getName();
                 final int    offset    = secondaryOffsets.get(name);
                 final int    dimension = provider.getDimension();
                 initialState = initialState.addAdditionalState(name, Arrays.copyOfRange(secondary, offset, offset + dimension));
             }
 
             return updateAdditionalStates(initialState);
 
         }
 
     }
 
     /** Adapt an {@link org.orekit.propagation.events.EventDetector}
      * to Hipparchus {@link org.hipparchus.ode.events.ODEEventDetector} interface.
      * @author Fabien Maussion
      */
     private class AdaptedEventDetector implements ODEEventDetector {
 
         /** Underlying event detector. */
         private final EventDetector detector;
 
         /** Underlying event handler.
          * @since 12.0
          */
         private final EventHandler handler;
 
         /** Time of the previous call to g. */
         private double lastT;
 
         /** Value from the previous call to g. */
         private double lastG;
 
         /** Build a wrapped event detector.
          * @param detector event detector to wrap
         */
         AdaptedEventDetector(final EventDetector detector) {
             this.detector = detector;
             this.handler  = detector.getHandler();
             this.lastT    = Double.NaN;
             this.lastG    = Double.NaN;
         }
 
         /** {@inheritDoc} */
         @Override
         public AdaptableInterval getMaxCheckInterval() {
             return s -> detector.getMaxCheckInterval().currentInterval(convert(s));
         }
 
         /** {@inheritDoc} */
         @Override
         public int getMaxIterationCount() {
             return detector.getMaxIterationCount();
         }
 
         /** {@inheritDoc} */
         @Override
         public BracketedUnivariateSolver<UnivariateFunction> getSolver() {
             return new BracketingNthOrderBrentSolver(0, detector.getThreshold(), 0, 5);
         }
 
         /** {@inheritDoc} */
         @Override
         public void init(final ODEStateAndDerivative s0, final double t) {
             detector.init(convert(s0), stateMapper.mapDoubleToDate(t));
             this.lastT = Double.NaN;
             this.lastG = Double.NaN;
         }
 
         /** {@inheritDoc} */
         public double g(final ODEStateAndDerivative s) {
             if (!Precision.equals(lastT, s.getTime(), 0)) {
                 lastT = s.getTime();
                 lastG = detector.g(convert(s));
             }
             return lastG;
         }
 
         /** {@inheritDoc} */
         public ODEEventHandler getHandler() {
 
             return new ODEEventHandler() {
 
                 /** {@inheritDoc} */
                 public Action eventOccurred(final ODEStateAndDerivative s, final ODEEventDetector d, final boolean increasing) {
                     return handler.eventOccurred(convert(s), detector, increasing);
                 }
 
                 /** {@inheritDoc} */
                 @Override
                 public ODEState resetState(final ODEEventDetector d, final ODEStateAndDerivative s) {
 
                     final SpacecraftState oldState = convert(s);
                     final SpacecraftState newState = handler.resetState(detector, oldState);
                     stateChanged(newState);
 
                     // main part
                     final double[] primary    = new double[s.getPrimaryStateDimension()];
                     stateMapper.mapStateToArray(newState, primary, null);
 
                     // secondary part
                     final double[][] secondary = new double[1][secondaryOffsets.get(SECONDARY_DIMENSION)];
                     for (final AdditionalDerivativesProvider provider : additionalDerivativesProviders) {
                         final String name      = provider.getName();
                         final int    offset    = secondaryOffsets.get(name);
                         final int    dimension = provider.getDimension();
                         System.arraycopy(newState.getAdditionalState(name), 0, secondary[0], offset, dimension);
                     }
 
                     return new ODEState(newState.getDate().durationFrom(getStartDate()),
                                         primary, secondary);
 
                 }
 
             };
         }
 
     }
 
     /** Adapt an {@link org.orekit.propagation.sampling.OrekitStepHandler}
      * to Hipparchus {@link ODEStepHandler} interface.
      * @author Luc Maisonobe
      */
     private class AdaptedStepHandler implements ODEStepHandler {
 
         /** Underlying handler. */
         private final OrekitStepHandler handler;
 
         /** Build an instance.
          * @param handler underlying handler to wrap
          */
         AdaptedStepHandler(final OrekitStepHandler handler) {
             this.handler = handler;
         }
 
         /** {@inheritDoc} */
         @Override
         public void init(final ODEStateAndDerivative s0, final double t) {
             handler.init(convert(s0), stateMapper.mapDoubleToDate(t));
         }
 
         /** {@inheritDoc} */
         @Override
         public void handleStep(final ODEStateInterpolator interpolator) {
             handler.handleStep(new AdaptedStepInterpolator(interpolator));
         }
 
         /** {@inheritDoc} */
         @Override
         public void finish(final ODEStateAndDerivative finalState) {
             handler.finish(convert(finalState));
         }
 
     }
 
     /** Adapt an Hipparchus {@link ODEStateInterpolator}
      * to an orekit {@link OrekitStepInterpolator} interface.
      * @author Luc Maisonobe
      */
     private class AdaptedStepInterpolator implements OrekitStepInterpolator {
 
         /** Underlying raw rawInterpolator. */
         private final ODEStateInterpolator mathInterpolator;
 
         /** Simple constructor.
          * @param mathInterpolator underlying raw interpolator
          */
         AdaptedStepInterpolator(final ODEStateInterpolator mathInterpolator) {
             this.mathInterpolator = mathInterpolator;
         }
 
         /** {@inheritDoc}} */
         @Override
         public SpacecraftState getPreviousState() {
             return convert(mathInterpolator.getPreviousState());
         }
 
         /** {@inheritDoc}} */
         @Override
         public boolean isPreviousStateInterpolated() {
             return mathInterpolator.isPreviousStateInterpolated();
         }
 
         /** {@inheritDoc}} */
         @Override
         public SpacecraftState getCurrentState() {
             return convert(mathInterpolator.getCurrentState());
         }
 
         /** {@inheritDoc}} */
         @Override
         public boolean isCurrentStateInterpolated() {
             return mathInterpolator.isCurrentStateInterpolated();
         }
 
         /** {@inheritDoc}} */
         @Override
         public SpacecraftState getInterpolatedState(final AbsoluteDate date) {
             return convert(mathInterpolator.getInterpolatedState(date.durationFrom(stateMapper.getReferenceDate())));
         }
 
         /** {@inheritDoc}} */
         @Override
         public boolean isForward() {
             return mathInterpolator.isForward();
         }
 
         /** {@inheritDoc}} */
         @Override
         public AdaptedStepInterpolator restrictStep(final SpacecraftState newPreviousState,
                                                     final SpacecraftState newCurrentState) {
             try {
                 final AbstractODEStateInterpolator aosi = (AbstractODEStateInterpolator) mathInterpolator;
                 return new AdaptedStepInterpolator(aosi.restrictStep(convert(newPreviousState),
                                                                      convert(newCurrentState)));
             } catch (ClassCastException cce) {
                 // this should never happen
                 throw new OrekitInternalError(cce);
             }
         }
 
     }
 
     /** Specialized step handler storing interpolators for ephemeris generation.
      * @since 11.0
      */
     private class StoringStepHandler implements ODEStepHandler, EphemerisGenerator {
 
         /** Underlying raw mathematical model. */
         private DenseOutputModel model;
 
         /** the user supplied end date. Propagation may not end on this date. */
         private AbsoluteDate endDate;
 
         /** Generated ephemeris. */
         private BoundedPropagator ephemeris;
 
         /** Last interpolator handled by the object.*/
         private  ODEStateInterpolator lastInterpolator;
 
         /** Set the end date.
          * @param endDate end date
          */
         public void setEndDate(final AbsoluteDate endDate) {
             this.endDate = endDate;
         }
 
         /** {@inheritDoc} */
         @Override
         public void init(final ODEStateAndDerivative s0, final double t) {
 
             this.model = new DenseOutputModel();
             model.init(s0, t);
 
             // ephemeris will be generated when last step is processed
             this.ephemeris = null;
 
             this.lastInterpolator = null;
 
         }
 
         /** {@inheritDoc} */
         @Override
         public BoundedPropagator getGeneratedEphemeris() {
             // Each time we try to get the ephemeris, rebuild it using the last data.
             buildEphemeris();
             return ephemeris;
         }
 
         /** {@inheritDoc} */
         @Override
         public void handleStep(final ODEStateInterpolator interpolator) {
             model.handleStep(interpolator);
             lastInterpolator = interpolator;
         }
 
         /** {@inheritDoc} */
         @Override
         public void finish(final ODEStateAndDerivative finalState) {
             buildEphemeris();
         }
 
         /** Method used to produce ephemeris at a given time.
          * Can be used at multiple times, updating the ephemeris to
          * its last state.
          */
         private void buildEphemeris() {
             // buildEphemeris was built in order to allow access to what was previously the finish method.
             // This now allows to call it through getGeneratedEphemeris, therefore through an external call,
             // which was not previously the case.
 
             // Update the model's finalTime with the last interpolator.
             model.finish(lastInterpolator.getCurrentState());
 
             // set up the boundary dates
             final double tI = model.getInitialTime();
             final double tF = model.getFinalTime();
             // tI is almost? always zero
             final AbsoluteDate startDate =
                             stateMapper.mapDoubleToDate(tI);
             final AbsoluteDate finalDate =
                             stateMapper.mapDoubleToDate(tF, this.endDate);
             final AbsoluteDate minDate;
             final AbsoluteDate maxDate;
             if (tF < tI) {
                 minDate = finalDate;
                 maxDate = startDate;
             } else {
                 minDate = startDate;
                 maxDate = finalDate;
             }
 
             // get the initial additional states that are not managed
             final DoubleArrayDictionary unmanaged = new DoubleArrayDictionary();
             for (final DoubleArrayDictionary.Entry initial : getInitialState().getAdditionalStatesValues().getData()) {
                 if (!isAdditionalStateManaged(initial.getKey())) {
                     // this additional state was in the initial state, but is unknown to the propagator
                     // we simply copy its initial value as is
                     unmanaged.put(initial.getKey(), initial.getValue());
                 }
             }
 
             // get the names of additional states managed by differential equations
             final String[] names      = new String[additionalDerivativesProviders.size()];
             final int[]    dimensions = new int[additionalDerivativesProviders.size()];
             for (int i = 0; i < names.length; ++i) {
                 names[i] = additionalDerivativesProviders.get(i).getName();
                 dimensions[i] = additionalDerivativesProviders.get(i).getDimension();
             }
 
             // create the ephemeris
             ephemeris = new IntegratedEphemeris(startDate, minDate, maxDate,
                                                 stateMapper, propagationType, model,
                                                 unmanaged, getAdditionalStateProviders(),
                                                 names, dimensions);
 
         }
 
     }
 
     /** Wrapper for resetting an integrator handlers.
      * <p>
      * This class is intended to be used in a try-with-resource statement.
      * If propagator-specific event handlers and step handlers are added to
      * the integrator in the try block, they will be removed automatically
      * when leaving the block, so the integrator only keeps its own handlers
      * between calls to {@link AbstractIntegratedPropagator#propagate(AbsoluteDate, AbsoluteDate).
      * </p>
      * @since 11.0
      */
     private static class IntegratorResetter implements AutoCloseable {
 
         /** Wrapped integrator. */
         private final ODEIntegrator integrator;
 
         /** Initial event detectors list. */
         private final List<ODEEventDetector> detectors;
 
         /** Initial step handlers list. */
         private final List<ODEStepHandler> stepHandlers;
 
         /** Simple constructor.
          * @param integrator wrapped integrator
          */
         IntegratorResetter(final ODEIntegrator integrator) {
             this.integrator   = integrator;
             this.detectors    = new ArrayList<>(integrator.getEventDetectors());
             this.stepHandlers = new ArrayList<>(integrator.getStepHandlers());
         }
 
         /** {@inheritDoc}
          * <p>
          * Reset event handlers and step handlers back to the initial list
          * </p>
          */
         @Override
         public void close() {
 
             // reset event handlers
             integrator.clearEventDetectors();
             detectors.forEach(integrator::addEventDetector);
 
             // reset step handlers
             integrator.clearStepHandlers();
             stepHandlers.forEach(integrator::addStepHandler);
 
         }
 
     }
 
 }