Re: [Orekit Developers] STM/Jacobians w.r.t. Keplerian Parameters

[MAISONOBE Luc <luc.maisonobe@c-s.fr>]

"Ward, Evan" <Evan.Ward@nrl.navy.mil> a écrit :

> Hi Christophe,
>
>
> On Thu, 2017-08-10 at 17:59 +0200, Christophe LE BRIS wrote:
>
> Hi,
>
> With PartialDerivativeEquations, STM are given wrt cartesian parameters
> only.
>
> If you want to have it wrt Keplerian parameters, you need to compute the
> Jacobian "dKep/Cart" with the method computeJacobianMeanWrtCartesian in
> the class KeplerianOrbit (on the final state) and then use it to change
> of basis of your STM (the STM is a linear transformation).
>
>
> Thanks for the reply. I tried your suggestion and it worked well,  
> once I made the tolerance a little tighter.
>
> What is PDE actually computing then when orbitType is not Cartesian?

I fear it only computes Jacobians of current Cartesian parameters with
respect to initial Cartesian parameters.

> I thought the mapper returned by  
> PartialDerivativeEquations.getMapper() took care of converting  
> orbital element representations since it calls  
> Orbit.getJacobianWrtCaresian() both when setting the initial STM and  
> when retrieving the STM. [1-2] Should I add some documentation  
> warning the user to never use the PDE class with non-Cartesian  
> elements?

Yes, you are rigtht, but internally in  
PartialDerivativesEquations.computeDerivatives
we clearly use Cartesian only. Also since 9.0, we use a new DSConverter class
to compute more accurately some derivatives (and also take care of the
orbit/attitude coupling we wanted to include since issue #200). This  
new converter
clearly switches to Cartesian only, this is an oversight (and the classe also
still refers to Jacobians being either 6x6 or 7x7 despite I removed  
this in 9.0).

So I don't know if the limitation has been introduces in 9.0 with the  
DSConverter,
or if it was there earlier due to  
PartialDerivativesEquations.computeDerivatives.

This limitation should be removed. I would in fact be happy with a solution
that completely rewrites this class from scratch and dumps it in favor
of a cleaner implementation (well, deprecate it first to help users switch).
I don't like this class and its clumsy API.

Evan, could you look at this? I am still on holidays for one week and  
really need
a break.

best regards,
Luc

> [1]  
> https://www.orekit.org/forge/projects/orekit/repository/revisions/master/entry/src/main/java/org/orekit/propagation/numerical/JacobiansMapper.java#L140
> [2]  
> https://www.orekit.org/forge/projects/orekit/repository/revisions/master/entry/src/main/java/org/orekit/propagation/numerical/JacobiansMapper.java#L182
>
> Best Regards,
> Evan
>
>
>
>
> Christophe
>
>
> Le 10/08/2017 à 17:24, Ward, Evan a écrit :
>
>
> Hi,
>
> I'm trying to compute the State Transition Matrix (STM) for Keplerian
> orbit w.r.t. Keplerian parameters. I'm not sure if I'm doing it right
> so I thought I'd post my question here. So I'm trying to compute
> dx(t)/dx(0) where x = {a, e, i,  arg. of perigee, RAAN, M (mean
> anomaly)}. According to Montenbruck & Gill (section 7.1.1 of Satellite
> Orbits) the result should be the identity matrix except for the
> dM(t)/da(0).  term. In Orekit I've set the orbitType to Keplerian and
> the positionAngleType to Mean, but the result looks very different
> from what I would expect. I've attached my code and included the
> output below. The code is in groovy and it should be able to run if
> you want to try it. Am I doing something wrong? Is this a bug?
>
> Initial State
> Keplerian parameters: {a: 6678137.0; e: 0.1; i: 50.0; pa: 0.0; raan:  
> 0.0; v: 0.0;}
> Final state
> Keplerian parameters: {a: 6678137.0; e: 0.1; i: 50.0; pa: 0.0; raan:  
> 0.0; v: 359.9999999999999;}
> STM
>          1.084033316          1048746.583     -1.881271601e-07        
>    338443.1765          217547.0804          689070.0095
>      8.986475977e-08        -0.4460115259      5.972999872e-14        
>  -0.2344750310        -0.1507176447        -0.5273227631
>     -5.987960454e-21      1.482147738e-14          1.008352980      
> -2.359223927e-15       0.003748479827      5.162537065e-15
>     -1.049794901e-06          19.17181914      -0.009257359011        
>    1.103560184        0.05508206389         -1.305994282
>      3.388131789e-21      9.503509091e-14        0.01440189399       
> 9.742207041e-15          1.017867705      2.688127498e-14
>      7.973387020e-09         -23.67118846      1.041684976e-12        
>  -0.8494761263        -0.5460327287         0.9198999327
> Expected dM(t)/da(t0)
> -1.411288501683835E-6
>
>
> Best Regards,
> Evan