The development of fixed-step higher-order variational integrators based on geometric integration methods is presented. These methods are symplectic, preserve energy in Hamiltonian conservative systems, and are highly accurate for long-term integration. By properly selecting a quadrature rule and control points in the polynomial approximation of the trajectory, a fast algorithm that reduces the number of computations of the gravitational force terms is constructed. Numerical simulations are presented for different scenarios, comparing Galerkin variational integrators against traditional fixed-step propagators used in astrodynamics applications. An error analysis is then performed, focusing on the implications of energy conservation and the accuracy of the methods. It is found that, under certain conditions, Galerkin methods are superior to nonsymplectic integrators for long-term orbital propagation, reducing simulation times significantly for long integration periods. This makes the methods suitable for long-term orbital dynamics applications about small bodies, such as asteroids.
Galerkin Variational Integrators for Orbit Propagation with Applications to Small Bodies
Journal of Guidance, Control, and Dynamics ; 42 , 2 ; 347-363
2018-11-26
17 pages
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
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