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

["Ward, Evan" <Evan.Ward@nrl.navy.mil>]

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 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?

[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
> >
> >