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Re: [Orekit Developers] status on second order derivatives

Hi all,

Here are some final updates about the derivatives and the velocity
problem in Eckstein-Hechler.

>> Evan Ward <evan.ward@nrl.navy.mil> a écrit :

>> To check that the initial orbit matching is causing the errors, I found
>> that if the initial orbit is shifted by a quarter period (or -0.75
>> period) that the EH ephemeris stays within 70 m of the numerical
>> propagator.
> For better fitting, we can always use the PropagatorConverter
> implementations : they adjust the initial parameters on a complete
> sample instead of only one point.

I have further studied this option and reached a state I consider now

The Eckstein-Hechler-Cartesian branch includes the latest fixes, as well
as some attempt to document the behaviour.

>> So IMHO we can either fit the velocity exactly at the epoch or fit the
>> orbit parameters and tolerate a small velocity discrepancy at the epoch
>> in return for an orbit closer to the numerical propagator. Both can work
>> with option 2.
> I definitely think option 2 is much simpler, so if you can find a way to
> meke it work, I would be very happy.

The solution implemented in this branch is the one proposed by Evan:
directly build a CartesianOrbit, and forget about any new specialized
orbit type.

Looking at several ways to fit the initial orbits, it appeared that was
has been done from the beginning (i.e. fit the circular parameters)
works pretty well, so I ave kept it. Furthermore, this means the new
Eckstein-Hechler propagator just propagates the exact same positions has
it has always done, it only output them as Cartesian.

So the circular orbit that are used in the equations of the model and
that are also used for the initialization are now only internal ones,
they are not output anymore.

I compared this initialization with the PropagatorConverter Pascal
created a few years ago, and which relies on a full sample and not a
single point, and indeed the result are pretty close. So our
initialization was good, and could be kept.

So if users rebuild circular parameters from the generated Cartesian
parameters, they will see a difference with respect to the initial orbit
they used for building the propagator, but I now consider these
differences to be normal and related to the velocity discrepancy we
observed. If we recompute just the position from the circular
parameters, they all match to sub-micrometer level (i.e. the position
computed from the initial circular parameters, the position extracted
from the propagated orbit at t = 0 and the position computed from
converting the propagated orbit at t = 0 to circular).

I have created an issue <https://www.orekit.org/forge/issues/180> and
solved it. I have also updated the wiki page on propagation

I think we could now merge branch Eckstein-Hechler-Cartesian (which
includes the branch position-velocity-acceleration) back to master.

What do you think ?

> For now, I have pushed the two branches I use for experiments. One is
> called EHOrbit and implements option 3, the other is called
> Eckstein-Hechler-Cartesian and implements option 2. In both cases, I
> have updated the tests as much as possible to match the accuracy
> achieved. For option 3, now all tests without exception do pass.
> Interpolation is very good but shiftedBy behaves strangely (I feel the
> error increases too fast for my taste). For option 2, four tests in
> EcksteinHechlerPropagatorTest fail, as explained in my previous post. If
> we could get them working, I think this branch would be a much better
> solution to merge in master.
>> Do you have access the reference publication for the EH propagator? I
>> think it may help to see how the propagator is initialized there.
> Unfortunately, no. The implementation was created from an appendix in
> the CNES 1995 book, not from the original paper. This book is not
> available anymore as far as I know. I will look again at it but don't
> think there is anything about initialization. The initialization process
> we used is a very simple fixed-point iteration as the model creates
> osculating parameters from mean parameters : so we iterate until the
> produced osculating match the initial orbit, currently in terms of
> circular parameters.

I have looked in the book. There was nothing about the initialization of
the model, only a few pages of raw equations without any explanation. If
you have access to this book (Spaceflight Dynamics - part I, 1995,
collaborative work from CNES, editor Jean-Pierre Carrou, ISBN
2.85428.376.7), the model is in pp 474-481.

best regards,

> best regards,
> Luc
>> Best Regards,
>> Evan
>>> So up to now, I was not able to have both initial orbit, propagated
>>> orbit and velocity correct. In all my tests, I had only two correct
>>> among the three.
>>>> 3. Create a combined orbit that has both the EH elements and the
>>>> position and velocity. This may be a bit confusing for the users since
>>>> the EH orbital elements are only define w.r.t. the EH propagation
>>>> model.
>>> In fact, as seen in the previous case, the orbital elements are also
>>> visible to the user as they are used to initialize the propagator from
>>> an osculating orbit (notwithstanding velocity). The hidden parameters
>>> are the mean parameters from wich EH computes the osculating ones.
>>>> In other words, if a user writes a method to use a Propagator (the base
>>>> interface, not one of its sub classes) then the user wouldn't be
>>>> able to
>>>> use the elements (a, e, i, ...) in the returned orbit since they
>>>> wouldn't know how the elements are defined. On the other hand, if the
>>>> user needs the EH parameters then I think this is the definition we
>>>> should choose. (IIUC this is what Luc is describing.)
>>> I tried it for the last few days (before switching to your suggestion
>>> number 2 above). It almost works but is quite complicated and I did
>>> not yet manage to solve a last problem.
>>> The way I've done it was to create an internal EHOrbit class extending
>>> CircularOrbit and overriding a few methods. At construction time it
>>> preserve the value of the circular osculating parameters (so initial
>>> orbit is preserved when propagating to same date), and it does not
>>> modify the mean parameters computation loop (so propagated orbit is
>>> consistent with other numerical propagators), and it additionally
>>> computes Cartesian parameters knowing about the derivatives (so it
>>> solves the initial problem). It's a bunch of code, but is quite
>>> straightforward thanks to the DerivativeStructure class which greatly
>>> simplifies derivatives computation.
>>> This however is not enough, and a few methods should be overriden too:
>>> shitfetBy and interpolate. Failing to overriding thme creates another
>>> type of inconsistency: the velocity of shifted or interpolated
>>> instances computed directly by the base CircularOrbit class is wrong.
>>> Overriding shiftedBy is trivial and works well. Overriding interpolate
>>> is difficult as it could be fed from several types of orbit in the
>>> sample, so I tried to rebuild the derivatives if the sample did not
>>> include them. This is a nightmare and I utterly failed. The problem is
>>> interpolate is automatically used for example when one creates an
>>> ephemeris from an EcksteinHechler propagator. It is a feature shared
>>> among all propagators and widely used.
>>> So I am confused now.
>>> I could attempt to reset the specialized EHOrbit class that knows
>>> about non-Keplerian effect when converting back and forth between
>>> circular and Cartesian, but I have yet to find how interpolate should
>>> work. Perhaps we could simply say that the specific implementation of
>>> interpolate in EHOrbit works *only* when the sample contains only
>>> EHOrbit instances and throws an exception otherwise. It seems fair to
>>> me as we cannot rebuild missing derivatives, and it would still work
>>> correctly in the regular case where people use consistently EHOrbit
>>> for a sample. In fact, it could probably be considered a general
>>> contract of the interpolate method to use only one type of orbits at a
>>> time and not to convert anything under the hood.
>>> Any thought ?
>>> Luc
>>>>>>> The problem may not hold for NumericalPropagator (I still have to
>>>>>>> check), because basically we do the computation the other way
>>>>>>> round. We
>>>>>>> start from x, y, z, vx, vy, vz and deduce a, e, ... from the
>>>>>>> mapping. So
>>>>>>> as long as our vx=dx/dt, vy=dy/dt, vz=dz/dt, the initial mapping
>>>>>>> will
>>>>>>> still hold.
>>>>>>>> It seems that if we add rates to all the elements then the
>>>>>>>> resulting
>>>>>>>> class could be classified as a Propagator.
>>>>>>> It is only a way to get a consistent (P, V), and as a propagator it
>>>>>>> would be really limited as it is a Taylor expansion. I would simply
>>>>>>> qualify it as a perturbed orbit allowing local expansion.
>>>>>> Extending the Taylor series expansion to higher order derivatives
>>>>>> makes
>>>>>> sense if we need to return the propagator's internal state, and the
>>>>>> satellite's PV in one consistent object. Is there a use case for
>>>>>> providing the propagator's internal state? I don't know, but I can't
>>>>>> think of any.
>>>>>> If we need to provide the user with acceleration as well as PV then I
>>>>>> agree that we need a bigger container class to hold the extra
>>>>>> information. Maybe the new PVACoordinates would be the right choice
>>>>> I agree this is a good place. However, I did not create an extra class
>>>>> for this either, I simply added a third vector to PVCoordinates. We
>>>>> can discuss this later, when the merge of the branch will be
>>>>> attempted.
>>>>>> instead of a PerturbedOrbit class since I don't think we would get
>>>>>> the
>>>>>> same extrapolation from a PerturbedOrbit stored in Keplerian vs
>>>>>> Cartesian elements. To put it another way, If I converted a
>>>>>> PerturbedKeplerianOrbit to a PerturbedCartesianOrbit would they both
>>>>>> follow the same path?
>>>>> At second order level, in the neighborhood of the matching date, yes
>>>>> they should. Differences should appear at the first ignored derivative
>>>>> level and build up from there.
>>>>>> I'm not against the PerturbedOrbit classes; I just want to make
>>>>>> sure we
>>>>>> don't choose a complex solution to a simple problem.
>>>>> You are right. I have a clear tendency to over-engineer things, this
>>>>> is why I ask for advice from time to time. This is the great force of
>>>>> collaborative development : people don't get stuck in their own errors
>>>>> too long.
>>>> I think these constructive discussions combine the best ideas from
>>>> everyone.
>>>>> So to be clear, here is the consensus :
>>>>>  - I will simplify what I have done to limit as much as possible
>>>>>    the changes to CircularOrbit.
>>>>>  - In this setting, orbits will not know about non-Keplerian effects.
>>>>>  - As this knowledge is needed for accurate and more importantly
>>>>>    consistent velocity computation, the mapping between orbital
>>>>> parameters
>>>>>    and Cartesian parameters will be precomputed by the propagators
>>>>>  - If the mapping is not precomputed and orbits are built from one
>>>>>    set of parameters only, then the mapping will be Keplerian only
>>>>>    and will be performed byt orbit classes just as it is now
>>>> If we decide to define the orbit returned from a Propagator
>>>> according to
>>>> option 3 above then I think this is a good plan to implement it.
>>>> Best Regards,
>>>> Evan
>>>>> best regards,
>>>>> Luc
>>>>>>>> There might be a case for
>>>>>>>> this intermediate level of fidelity/speed, but is it worth the
>>>>>>>> added
>>>>>>>> complexity? Especially since we already have one that is fast (the
>>>>>>>> Orbit
>>>>>>>> class) and one that is precise (the Propagator classes). Maybe I'm
>>>>>>>> still
>>>>>>>> not understanding your proposal.
>>>>>>> I detected the problem when checking some pointing attitude modes
>>>>>>> that
>>>>>>> are related to spacecraft velocity (alignment of the spacecraft axis
>>>>>>> with ground drift for Earth observation). This mode transforms
>>>>>>> something
>>>>>>> that is a derivative (velocity) into a regular non-differentiated
>>>>>>> value
>>>>>>> (an angle). So we go up one order of derivation. For such modes, a
>>>>>>> wrong
>>>>>>> velocity induces a wrong angle and a wrong acceleration induces a
>>>>>>> wrong
>>>>>>> angular rate. As the angular rate is used for time shift, I needed
>>>>>>> it to
>>>>>>> be accurate.
>>>>>>> You also mentioned issues with Doppler which would also occur.
>>>>>>> We do need accurate velocity, and we do need a velocity that is
>>>>>>> consistent with the derivative of the position.
>>>>>> Definitely agree that getting the velocity correct is important.
>>>>>> Thanks
>>>>>> again for all the work you've put into solving this bug.
>>>>>> Best Regards,
>>>>>> Evan
>>>>>>> best regards,
>>>>>>> Luc
>>>>>>>> Best Regards,
>>>>>>>> Evan
>>>>>>>>>> Then we wouldn't have to modify the existing set of Orbit
>>>>>>>>>> classes, and
>>>>>>>>>> the user would see the correct osculating P/V. (This might be
>>>>>>>>>> equivalent
>>>>>>>>>> to your second approach.)
>>>>>>>>>> As far as where to put the code, it seems like the conversion
>>>>>>>>>> code would
>>>>>>>>>> be specific to the internal state representation used by the
>>>>>>>>>> propagator,
>>>>>>>>>> so I think it makes sense to keep the code as private to the
>>>>>>>>>> propagator.
>>>>>>>>>> Though if you think there would be other uses for the
>>>>>>>>>> conversion, I
>>>>>>>>>> think a public static factory method would work well.
>>>>>>>>> Yes, the conversion code is propagator dependent. The first
>>>>>>>>> implementation I played with is Eckstein-Hechler propagator,
>>>>>>>>> and it
>>>>>>>>> definitely is Eckstein-Hechler specific (it's a simple
>>>>>>>>> derivation of
>>>>>>>>> the original equations, so each time we did compute something like
>>>>>>>>> e =
>>>>>>>>> a * c + b * d, now we also have another statement to compute
>>>>>>>>> eDot =
>>>>>>>>> aDot * c + a * dCot + bDot * d + b * dDot). For numerical
>>>>>>>>> propagator
>>>>>>>>> we already have the derivatives since we start from the
>>>>>>>>> derivatives
>>>>>>>>> and integrate them, so its even simpler. For DSST, this will be
>>>>>>>>> a mix
>>>>>>>>> as the mean elements are integrated and the short periodics
>>>>>>>>> terms are
>>>>>>>>> computed from Fourier coefficients which are straightforward to
>>>>>>>>> differentiate. For ephemeris-based propagator, we will need to
>>>>>>>>> compute
>>>>>>>>> the derivatives of the underlying polynomials, which is also
>>>>>>>>> straightforward.
>>>>>>>>>> Thanks Luc for finding this issue and doing the analysis. I can
>>>>>>>>>> see how
>>>>>>>>>> this would be an issue when computing the Doppler as well as time
>>>>>>>>>> shifting.
>>>>>>>>> your welcome
>>>>>>>>> best regards,
>>>>>>>>> Luc
>>>>>>>>>> Best Regards,
>>>>>>>>>> Evan
>>>>>>>>>> On 10/29/2014 06:57 AM, MAISONOBE Luc wrote:
>>>>>>>>>>> Hi Paul,
>>>>>>>>>>> paulcefo <paulcefo@buffalo.edu> a écrit :
>>>>>>>>>>>> Luc,
>>>>>>>>>>>> Do I correctly understand that your concern is that Keplerian
>>>>>>>>>>>> transformations do apply outside the osculating space?
>>>>>>>>>>> The problem I had was that we did use Keplerian-only expression
>>>>>>>>>>> to set up local Taylor expansions around the current point (a
>>>>>>>>>>> few
>>>>>>>>>>> seconds away). This was slightly wrong when all the parameters
>>>>>>>>>>> were
>>>>>>>>>>> time-dependent and not only the anomaly was time-dependent. Of
>>>>>>>>>>> course,
>>>>>>>>>>> the error increasing with the time offset with respect to the
>>>>>>>>>>> central
>>>>>>>>>>> date at which the Taylor expansion is built. The fix was
>>>>>>>>>>> simply to
>>>>>>>>>>> not forget the derivatives of these other parameters.
>>>>>>>>>>> This Taylor expansion feature is a built-in feature available in
>>>>>>>>>>> all
>>>>>>>>>>> Orekit orbits, it typically allows to do computation in the
>>>>>>>>>>> vicinity of
>>>>>>>>>>> an already computed point without needed to trigger a complete
>>>>>>>>>>> propagator.
>>>>>>>>>>> It can even be used for some computation inside the run of a
>>>>>>>>>>> propagator,
>>>>>>>>>>> as for example when the higher level propagator takes care of
>>>>>>>>>>> the long
>>>>>>>>>>> term propagation and at each step we need some additional points
>>>>>>>>>>> surrounding the current step to compute attitude evolution in
>>>>>>>>>>> some
>>>>>>>>>>> specific modes.
>>>>>>>>>>> My concern was how to implement this fix in our current
>>>>>>>>>>> architecture,
>>>>>>>>>>> and more precisely were to put the code: in an existing class
>>>>>>>>>>> or in
>>>>>>>>>>> a dedicated class which would be used only by propagators.
>>>>>>>>>>> best regards,
>>>>>>>>>>> Luc
>>>>>>>>>>>> Paul
>>>>>>>>>>>> -- 
>>>>>>>>>>>> Dr. Paul J. Cefola
>>>>>>>>>>>> Consultant in Aerospace Systems, Spaceflight Mechanics, &
>>>>>>>>>>>> Astrodynamics
>>>>>>>>>>>> Adjunct Faculty, Dept. of Mechanical and Aerospace Engineering,
>>>>>>>>>>>> University at Buffalo (SUNY)
>>>>>>>>>>>> 4 Moonstone Way
>>>>>>>>>>>> Vineyard Haven, MA 02568
>>>>>>>>>>>> USA
>>>>>>>>>>>> 508-696-1884 (phone on Martha's Vineyard)
>>>>>>>>>>>> 978-201-1393 (cell)
>>>>>>>>>>>> paulcefo@buffalo.edu
>>>>>>>>>>>> paul.cefola@gmail.com
>>>>>>>>>>>> On 10/29/2014 6:02 am, MAISONOBE Luc wrote:
>>>>>>>>>>>>> Hello,
>>>>>>>>>>>>> As some of you may be aware, I have been working for a few
>>>>>>>>>>>>> months on
>>>>>>>>>>>>> second order derivatives in the git branch
>>>>>>>>>>>>> position-velocity-acceleration. This work is still ongoing but
>>>>>>>>>>>>> I hope
>>>>>>>>>>>>> to finish it for 7.0 and merge the branch back to master soon.
>>>>>>>>>>>>> For
>>>>>>>>>>>>> now, there are still failing tests so I can't do it.
>>>>>>>>>>>>> This change should allow us to reach several goals :
>>>>>>>>>>>>> - improved accuracy in shiftedBy methods
>>>>>>>>>>>>> - improved accuracy in interpolators (with user-defined
>>>>>>>>>>>>>   choices to use or not first and second derivatives
>>>>>>>>>>>>>   from the sample)
>>>>>>>>>>>>> - improved accuracy in attitude
>>>>>>>>>>>>> - removal of ugly hidden finite differences in some classes
>>>>>>>>>>>>>   (most notably attitude modes) with hard-coded steps
>>>>>>>>>>>>> - hopefully faster Earth transforms, by replacing Hermite
>>>>>>>>>>>>>   interpolation with single point extrapolation
>>>>>>>>>>>>> - availability of non-Keplerian acceleration everywhere
>>>>>>>>>>>>> - availability of angular acceleration in attitude and frames
>>>>>>>>>>>>> - proper composition of dynamics in frames
>>>>>>>>>>>>> - possibility to propagate orbits in non-inertial frames
>>>>>>>>>>>>> - possibility to propagate orbits without a central body
>>>>>>>>>>>>>   (interplanetary missions, Lagrange point missions, ...)
>>>>>>>>>>>>> There is one point that bothers me right now. As I removed
>>>>>>>>>>>>> some of
>>>>>>>>>>>>> the
>>>>>>>>>>>>> ugly finite differences, some non-regression tests started to
>>>>>>>>>>>>> fail. I
>>>>>>>>>>>>> finally found the raw cause of these failures and was
>>>>>>>>>>>>> surprised to
>>>>>>>>>>>>> discover an old bug in the way we use the osculating orbits
>>>>>>>>>>>>> produced
>>>>>>>>>>>>> by the Eckstein-Hechler analytical propagator. This propagator
>>>>>>>>>>>>> takes
>>>>>>>>>>>>> zonal terms into account, and produces directly circular
>>>>>>>>>>>>> parameters a,
>>>>>>>>>>>>> ex, ey, ... When we compute anything related to geometry, we
>>>>>>>>>>>>> compute
>>>>>>>>>>>>> Cartesian coordinates using the Orbit getPVCoordinates method.
>>>>>>>>>>>>> As the
>>>>>>>>>>>>> Orbit classes do not know anything about the perturbation, the
>>>>>>>>>>>>> (P, V)
>>>>>>>>>>>>> pair does in fact implicitly relies on Keplerian-only
>>>>>>>>>>>>> expressions. So
>>>>>>>>>>>>> the velocity part is *not* consistent with the derivative of
>>>>>>>>>>>>> the
>>>>>>>>>>>>> position. The real derivative of the position takes the
>>>>>>>>>>>>> non-Keplerian
>>>>>>>>>>>>> effects into account which are ignored by getPVCoordinates.
>>>>>>>>>>>>> The
>>>>>>>>>>>>> difference is small, but as the tests threshold were
>>>>>>>>>>>>> deliberatly very
>>>>>>>>>>>>> tight, the tests started to fail when the various pointing
>>>>>>>>>>>>> directions
>>>>>>>>>>>>> were not computed anymore from finite differences mainly
>>>>>>>>>>>>> involving
>>>>>>>>>>>>> position and when they relied on the computed velocity. So the
>>>>>>>>>>>>> problem
>>>>>>>>>>>>> already happens in the master branch, it is not specific to
>>>>>>>>>>>>> the
>>>>>>>>>>>>> introduction of acceleration (it was just detected here during
>>>>>>>>>>>>> testing).
>>>>>>>>>>>>> The solution is in fact quite simple. If an orbit has been
>>>>>>>>>>>>> produced by
>>>>>>>>>>>>> a non-Keplerian propagator, the propagator already knows about
>>>>>>>>>>>>> the
>>>>>>>>>>>>> derivatives of the orbital elements (which are circular in the
>>>>>>>>>>>>> Eckstein-Hechler model case but can be any kind of
>>>>>>>>>>>>> parameters for
>>>>>>>>>>>>> other propagators). The propagator should therefore provide
>>>>>>>>>>>>> these
>>>>>>>>>>>>> derivatives to the orbit so they can be used in the
>>>>>>>>>>>>> PVCoordinates
>>>>>>>>>>>>> conversion. The code is very simple and straightforward. I
>>>>>>>>>>>>> have
>>>>>>>>>>>>> checked this and got very interesting results with
>>>>>>>>>>>>> Eckstein-Hechler/Circular, as for example a simple
>>>>>>>>>>>>> interpolation over
>>>>>>>>>>>>> a 900s arc with proper velocity/acceleration has a 88m error
>>>>>>>>>>>>> with two
>>>>>>>>>>>>> base points now whereas it was 5162 m before (and 0.02m vs
>>>>>>>>>>>>> 650m for 3
>>>>>>>>>>>>> points, 1.0e-5m vs 259m for 4 points).
>>>>>>>>>>>>> Here is what bothers me:
>>>>>>>>>>>>> Should we create specialized classes for perturbed orbits or
>>>>>>>>>>>>> should we
>>>>>>>>>>>>> simply add a constructor to the existing orbits with the
>>>>>>>>>>>>> parameters
>>>>>>>>>>>>> derivatives and set them to 0 when they are not known?
>>>>>>>>>>>>> For my tests, I created PerturbedCircularOrbit which extends
>>>>>>>>>>>>> CircularOrbit and override the protected initPVCoordinates
>>>>>>>>>>>>> method and
>>>>>>>>>>>>> the public shiftedBy and interpolate methods. I could also
>>>>>>>>>>>>> have
>>>>>>>>>>>>> simply
>>>>>>>>>>>>> moved everything into CircularOrbit with a new constructor.
>>>>>>>>>>>>> I do not like much the PerturbedXxxxOrbit approach, as it
>>>>>>>>>>>>> forces to
>>>>>>>>>>>>> create also additional entries in the OrbitType enum with
>>>>>>>>>>>>> additional
>>>>>>>>>>>>> converters and it becomes awkward if for example a user
>>>>>>>>>>>>> configures a
>>>>>>>>>>>>> NumericalPropagator to generate XxxxOrbit, despite this
>>>>>>>>>>>>> propagator
>>>>>>>>>>>>> will in fact really generate PerturbedXxxOrbit because it is
>>>>>>>>>>>>> what a
>>>>>>>>>>>>> Numerical propagator is for. So there should be either an
>>>>>>>>>>>>> internal
>>>>>>>>>>>>> modification of the user setting from OrbitType.XXXX to
>>>>>>>>>>>>> OrbitType.PERTURBED_XXXX or an error triggered which would
>>>>>>>>>>>>> invalidate
>>>>>>>>>>>>> *all* current user code as it would become forbiddent to
>>>>>>>>>>>>> generate
>>>>>>>>>>>>> XXXX
>>>>>>>>>>>>> orbits now.
>>>>>>>>>>>>> On the other hand, the drawback of modifying the existing
>>>>>>>>>>>>> classes to
>>>>>>>>>>>>> hold the non-Keplerian derivatives is that they will consume
>>>>>>>>>>>>> more
>>>>>>>>>>>>> memory. I don't think it is a problem with current computers.
>>>>>>>>>>>>> In any case, initial orbits created directly from user code
>>>>>>>>>>>>> or by
>>>>>>>>>>>>> reading files would not include the derivatives and therefore
>>>>>>>>>>>>> will be
>>>>>>>>>>>>> built as usual (by calling the unmodified classes in the first
>>>>>>>>>>>>> approach, or by using the already existing constructors in the
>>>>>>>>>>>>> second
>>>>>>>>>>>>> approach, assuming these constructors will automatically set
>>>>>>>>>>>>> the
>>>>>>>>>>>>> derivatives to Keplerian-only values). In any case, full-blown
>>>>>>>>>>>>> perturbed orbits will be created internally by Orekit
>>>>>>>>>>>>> propagators,
>>>>>>>>>>>>> which can easily be modified to provide the derivatives they
>>>>>>>>>>>>> know (by
>>>>>>>>>>>>> creating instances of the new derived classes in the first
>>>>>>>>>>>>> approach,
>>>>>>>>>>>>> or by using new constructors with additional parameters in the
>>>>>>>>>>>>> second
>>>>>>>>>>>>> approach).
>>>>>>>>>>>>> My humble opinion would be to use the second approach to solve
>>>>>>>>>>>>> this
>>>>>>>>>>>>> bug. I will probably do this in the
>>>>>>>>>>>>> position-velocity-acceleration
>>>>>>>>>>>>> branch so it will include accelerations right from the start
>>>>>>>>>>>>> and will
>>>>>>>>>>>>> be merged to master at the same time as the rest of the
>>>>>>>>>>>>> branch. Of
>>>>>>>>>>>>> course, this will be a dedicated commits (Git branches are
>>>>>>>>>>>>> great!).
>>>>>>>>>>>>> What do you think ?
>>>>>>>>>>>>> best regards,
>>>>>>>>>>>>> Luc
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