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1992•Symposium - International Astronomical UnionOpen access

Symplectic Integrators for Hamiltonian Systems: Basic Theory

Haruo Yoshida

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Abstract

Symplectic integrators are numerical integration methods for Hamiltonian systems, which conserves the symplectic 2-form exactly. With use of symplectic integrators there is no secular increase in the error of the energy because of the existence of a conserved quantity closed to the original Hamiltonian. Higher order symplectic integrators are obtained by a composition of 2nd order ones.

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Symplectic integrators are numerical integration methods for Hamiltonian systems, which conserves the symplectic 2-form exactly. With use of symplectic integrators there is no secular increase in the error of the energy because of the existence of a conserved quantity closed to the original Hamiltonian. Higher order symplectic integrators are obtained by a composition of 2nd order ones.

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Available abstract

Symplectic integrators are numerical integration methods for Hamiltonian systems, which conserves the symplectic 2-form exactly. With use of symplectic integrators there is no secular increase in the error of the energy because of the existence of a conserved quantity closed to the original Hamiltonian. Higher order symplectic integrators are obtained by a composition of 2nd order ones.

Key concepts: Symplectic geometry, Symplectic integrator, Variational integrator, Hamiltonian system, Integrator, Mathematics, Hamiltonian (control theory), Superintegrable Hamiltonian system

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