Fundamental limits on spacecraft orbit uncertainty and distribution propagation

doi:10.1007/BF03256503

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Title:	Fundamental limits on spacecraft orbit uncertainty and distribution propagation
Authors:	Hsiao, Fu-yuen;Scheeres, D.J.;Park;Villac;Maruskin
Contributors:	淡江大學航空太空工程學系
Date:	2006-07
Issue Date:	2011-10-18 20:45:56 (UTC+8)
Publisher:	Springer
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.
Relation:	Journal of the Astronautical Sciences 54(3), pp.505-523
DOI:	10.1007/BF03256503
Appears in Collections:	[Graduate Institute & Department of Aerospace Engineering] Journal Article

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