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Structure Preserving Schemes for Birkhoff Systems

In: Symplectic Geometric Algorithms for Hamiltonian Systems

Author

Listed:
  • Kang Feng

    (Institute of Computational Mathematics and Scientific/Engineering Computing)

  • Mengzhao Qin

    (Institute of Computational Mathematics and Scientific/Engineering Computing)

Abstract

A universal symplectic structure for a Newtonian system including nonconservative cases can be constructed in the framework of Birkhoffian generalization of Hamiltonian mechanics. In this chapter, the symplectic geometry structure of Birkhoffian system is discussed, and the symplecticity of Birkhoffian phase flow is presented. Based on these properties, a way to construct symplectic schemes for Birkhoffian systems by the generating function method is explained[SSQS07],[SQ03].

Suggested Citation

  • Kang Feng & Mengzhao Qin, 2010. "Structure Preserving Schemes for Birkhoff Systems," Springer Books, in: Symplectic Geometric Algorithms for Hamiltonian Systems, chapter 0, pages 617-639, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-01777-3_16
    DOI: 10.1007/978-3-642-01777-3_16
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