A sixth-order accurate scheme for solving two-point boundary value problems in astrodynamics

Authors: Armellin, Roberto; Topputo, Francesco¹

Source: Celestial Mechanics and Dynamical Astronomy, Volume 96, Numbers 3-4, November 2006 , pp. 289-309(21)

Publisher: Springer

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Abstract:

A sixth-order accurate scheme is presented for the solution of ODE systems supplemented by two-point boundary conditions. The proposed integration scheme is a linear multi-point method of sixth-order accuracy successfully used in fluid dynamics and implemented for the first time in astrodynamics applications. A discretization molecule made up of just four grid points attains a O(h ⁶) accuracy which is beyond the first Dahlquist's stability barrier. Astrodynamics applications concern the computation of libration point halo orbits, in the restricted three- and four-body models, and the design of an optimal control strategy for a low thrust libration point mission.

Keywords: Non-linear boundary value problem; Restricted three-body problem; Bicircular four-body problem; Halo orbits

Document Type: Research article

DOI: 10.1007/s10569-006-9047-4

Affiliations: 1: Email: topputo@aero.polimi.it