Numerical integration of dynamical systems with Lie series |
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| Authors: | D Bancelin D Hestroffer W Thuillot |
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| Institution: | 1.IMCCE, Paris Observatory, CNRS, UPMC,Paris,France |
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| Abstract: | The integration of the equations of motion in gravitational dynamical systems—either in our Solar System or for extra-solar
planetary systems—being non integrable in the global case, is usually performed by means of numerical integration. Among the
different numerical techniques available for solving ordinary differential equations, the numerical integration using Lie
series has shown some advantages. In its original form (Hanslmeier and Dvorak, Astron Astrophys 132, 203 1984), it was limited to the N-body problem where only gravitational interactions are taken into account. We present in this paper a generalisation of the
method by deriving an expression of the Lie terms when other major forces are considered. As a matter of fact, previous studies
have been done but only for objects moving under gravitational attraction. If other perturbations are added, the Lie integrator
has to be re-built. In the present work we consider two cases involving position and position-velocity dependent perturbations:
relativistic acceleration in the framework of General Relativity and a simplified force for the Yarkovsky effect. A general
iteration procedure is applied to derive the Lie series to any order and precision. We then give an application to the integration
of the equation of motions for typical Near-Earth objects and planet Mercury. |
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