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High order symplectic integrators for perturbed Hamiltonian systems

  • Jacques Laskar
  • Philippe Robutel
Article

Abstract

A family of symplectic integrators adapted for the integration of perturbed Hamiltonian systems of the form H = A + εB 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 Opε + τ2ε2), where τ 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 Opε +τ4ε2). The performances of these integrators are compared for the simple pendulum and the planetary three-body problem of Sun–Jupiter–Saturn.

symplectic integrators Hamiltonian systems planetary motion Lie algebra 

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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Jacques Laskar
  • Philippe Robutel

There are no affiliations available

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