Abstract In this paper we present and review a number of fundamental constraints that exist on the propagation of orbit uncertainty and phase volume flows in astrodynamics. These constraints arise due to the Hamiltonian nature of spacecraft dynamics. First we review the role of integral invariants and their connection to orbit uncertainty, and show how they can be used to formally solve the diffusion-less Fokker-Plank equation for a spacecraft probability density function. Then, we apply Gromov’s Non-Squeezing Theorem, a recent advance in symplectic topology, to find a previously unrecognized fundamental constraint that exists on general, nonlinear mappings of orbit distributions. Specifically, for a given orbit distribution, it can be shown that the projection of future orbit uncertainties in each coordinate-momentum pair describing the system must be greater than or equal to a fundamental limit, called the symplectic width. This implies that there is always a fundamental limit to which we can know a spacecraft’s future location in its coordinate and conjugate momentum space when mapped forward in time from an initial covariance distribution. This serves as an “uncertainty” principle for spacecraft uncertainty distributions.


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    Title :

    Fundamental limits on spacecraft orbit uncertainty and distribution propagation


    Contributors:


    Publication date :

    2006




    Type of media :

    Article (Journal)


    Type of material :

    Print


    Language :

    English



    Classification :

    Local classification TIB:    770/7040
    BKL:    55.60 Raumfahrttechnik



    Fundamental limits on spacecraft orbit uncertainty and distribution propagation

    Scheeres, D. J. / Hsiao, F.-Y. / Park, R. S. et al. | Springer Verlag | 2006



    Fundamental Limits on Spacecraft Orbit Uncertainty and Distribution Propagation

    Scheeres, D. J. / Hsiao, F.-Y. / Park, R. S. et al. | British Library Conference Proceedings | 2006


    Fundamental Limits on Spacecraft Orbit Uncertainty and Distribution Propagation (AAS 05-471)

    Scheeres, D. J. / Hsiao, F.-Y. / Park, R. S. et al. | British Library Conference Proceedings | 2006