Nonlinear Semi-Analytic Methods for Spacecraft Trajectory Design, Control, and Navigation

Details Nonlinear Semi-Analytic Methods for Spacecraft Trajectory Design, Control, and Navigation Nonlinear Semi-Analytic Methods for Spacecraft Trajectory Design, Control, and Navigation

Feb 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007aipc..886...78p&link_type=abstract

NEW TRENDS IN ASTRODYNAMICS AND APPLICATIONS III. AIP Conference Proceedings, Volume 886, pp. 78-89 (2007).

Nonlinear Sciences

Chaotic Dynamics

Spaceborne And Space Research Instruments, Apparatus, And Components, Chaotic Dynamics, Nonlinear Dynamics And Chaos

Scientific paper

In this paper, we present a review of nonlinear semi-analytic methods for spacecraft trajectory design, control, and navigation. We first discuss previous and recent development of higher-order relative dynamics theory for a general dynamical system and stress the importance of incorporating the system nonlinearity in the model. For a given reference trajectory, the localized nonlinear dynamics is represented by the higher order state transition tensors, which are computed numerically by integrating the higher order Taylor series terms. We then analytically propagate the a priori Gaussian probability density function via solutions of the Fokker-Planck equations and compute the associated moments, such as the mean and covariance matrix. Using this analytic realization of the system dynamics and statistics, we derive analytic methods which allows one to propagate, control, and estimate the spacecraft trajectory while incorporating the system nonlinearity. As examples, three-body problems are considered and the results are compared with first-order (linear) methods.

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