中国物理B ›› 2011, Vol. 20 ›› Issue (3): 34501-034501.doi: 10.1088/1674-1056/20/3/034501

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Geometric formulations and variational integrators of discrete autonomous Birkhoff systems

郭永新1, 刘畅2, 刘世兴3   

  1. (1)College of Physics, Liaoning University, Shenyang 110036, China; (2)Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China; (3)Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China;College of Physics, Liaoning University, Shenyang 110036, China
  • 收稿日期:2010-06-22 修回日期:2010-09-28 出版日期:2011-03-15 发布日期:2011-03-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 10872084 and 10932002), the Research Program of Higher Education of Liaoning Province, China (Grant No. 2008S098), the Program of Supporting Elitists of Higher Education of

Geometric formulations and variational integrators of discrete autonomous Birkhoff systems

Liu Shi-Xing(刘世兴)a)b),Liu Chang(刘畅)a),and Guo Yong-Xin(郭永新)b)†   

  1. a Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China; b College of Physics, Liaoning University, Shenyang 110036, China
  • Received:2010-06-22 Revised:2010-09-28 Online:2011-03-15 Published:2011-03-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 10872084 and 10932002), the Research Program of Higher Education of Liaoning Province, China (Grant No. 2008S098), the Program of Supporting Elitists of Higher Education of Liaoning Province, China (Grant No. 2008RC20), the Program of Constructing Liaoning Provincial Key Laboratory, China (Grant No. 2008403009), the Foundation Research Plan of Liaoning educational Bureau, China (Grant No. L2010147), and the Youth fund of Liaoning University, China (Grant No. 2008LDQN04).

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摘要： The variational integrators of autonomous Birkhoff systems are obtained by the discrete variational principle. The geometric structure of the discrete autonomous Birkhoff system is formulated. The discretization of mathematical pendulum shows that the discrete variational method is as effective as symplectic scheme for the autonomous Birkhoff systems.

关键词: autonomous Birkhoff syetem, discrete variational principle, variational integrators

Abstract: The variational integrators of autonomous Birkhoff systems are obtained by the discrete variational principle. The geometric structure of the discrete autonomous Birkhoff system is formulated. The discretization of mathematical pendulum shows that the discrete variational method is as effective as symplectic scheme for the autonomous Birkhoff systems.

Key words: autonomous Birkhoff syetem, discrete variational principle, variational integrators

中图分类号:  (Lagrangian and Hamiltonian mechanics)

  • 45.20.Jj