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Abstract. Symplectic integration algorithms have become popular in recent years in long-term orbital integrations because these algorithms enforce certain conservation laws that are intrinsic to Hamiltonian systems. For problems with large variations in timescale, it is desirable to use a variable timestep. However, naively varying the timestep destroys the desirable properties of symplectic integrators. We discuss briefly the idea that choosing the timestep in a time symmetric manner can improve the performance of variable timestep integrators. Then we present a symplectic integrator which is based on decomposing the force into components and applying the component forces with different timesteps. This multiple timescale symplectic integrator has all the desirable properties of the constant timestep symplectic integrators. 1. Symplectic Integrators Long-term numerical integrations play an important role in our understanding of the dynamical evolution of many astrophysical systems (see, e.g., Duncan, these proceedings, for a review of solar-system integrations). An essential tool for long-term integrations is a fast and accurate integration algorithm. Symplectic integration algorithms (SIAs) have become popular in recent years because the Newtonian gravitational N-body problem is a Hamiltonian problem and SIAs enforce certain conservation laws that are intrinsic to Hamiltonian systems (see Sanz-Serna & Calvo 1994 for a general introduction to SIAs). For an autonomous Hamiltonian system, the equations of motion are dw/dt = {w,H}, (1) where H(w) is the explicitly time-independent Hamiltonian, w = (q,p) are the 2d canonical phase-space coordinates, { , } is the Poisson bracket, and d( = 3N

Year: 1997

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oai:CiteSeerX.psu:10.1.1.316.1998

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