High order symplectic integrators for perturbed Hamiltonian systems |
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Authors: | Jacques Laskar Philippe Robutel |
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Institution: | (1) Department of Astronomy, Nanjing University, Nanjing, 210093, China |
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Abstract: | A family of symplectic integrators adapted for the integration of perturbed Hamiltonian systems of the form H = A +![thinsp](/content/gw5054g5046600m5/xxlarge8201.gif) B was given in (McLachlan, 1995). We give here a constructive proof that for all integer p, such integrator exists, with only positive steps, and with a remainder of order O( p + 2 2), where is the stepsize of the integrator. Moreover, we compute the analytical expressions of the leading terms of the remainders at all orders. We show also that for a large class of systems, a corrector step can be performed such that the remainder becomes O( p + 4 2). The performances of these integrators are compared for the simple pendulum and the planetary three-body problem of Sun–Jupiter–Saturn. |
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Keywords: | symplectic integrators Hamiltonian systems planetary motion Lie algebra |
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