On the solution of the Fokker-Planck equation without diffusion for uncertainty propagation in orbital dynamics

Acciarini, Giacomo and Greco, Cristian and Vasile, Massimiliano (2020) On the solution of the Fokker-Planck equation without diffusion for uncertainty propagation in orbital dynamics. In: 2020 AAS/AIAA Astrodynamics Specialist Conference, 2020-08-09 - 2020-08-12, Lake Tahoe Resort Hotel.

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Abstract

This paper presents a method to transform the Fokker-Planck partial differential equation without diffusion into a set of linear ordinary differential equations. This is achieved by first representing the probability density function (pdf) through a summation of time-varying coefficients and spatial basis functions and by then employing Galerkin projection in the Fokker-Planck equation. We show that this method, compared to other numerical techniques, can bring several advantages in the field of uncertainty propagation in orbital dynamics, by not only allowing to retain the entire shape of the pdf through time but also to very rapidly compute the pdf at any time and with any initial condition, once that the spatial support is chosen and several time-independent integrals on the chosen support are computed.

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