Explicit Symplectic Integrator for Rotating Satellites |
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| Authors: | S?awomir Breiter Marcin Buciora |
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| Institution: | (1) Astronomical Observatory, A. Mickiewicz University, Słoneczna 36, PL 60-286 Poznań, Poland |
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| Abstract: | An explicit symplectic integrator is constructed for the problem of a rotating planetary satellite on a Keplerian orbit. The
spin vector is fixed perpendicularly to the orbital plane. The integrator is constructed according to the Wisdom-Holman approach:
the Hamiltonian is separated in two parts so that one of them is multiplied by a small parameter. The parameter depends on
the satellite’s shape or the eccentricity of its orbit. The leading part of the Hamiltonian for small eccentricity orbits
is similar to the simple pendulum and hence integrable; the perturbation does not depend on angular momentum which implies
a trivial ‘kick’ solution. In spite of the necessity to evaluate elliptic function at each step, the explicit symplectic integrator
proves to be quite efficient.
This revised version was published online in July 2006 with corrections to the Cover Date. |
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| Keywords: | numerical methods symplectic integrators satellite rotation |
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