Geometric formulations and variational integrators of discrete autonomous Birkhoff systems

doi:10.1088/1674-1056/20/3/034501

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.

Keywords: autonomous Birkhoff syetem discrete variational principle variational integrators

Received: 22 June 2010
Revised: 28 September 2010
Accepted manuscript online:

PACS:

45.20.Jj

(Lagrangian and Hamiltonian mechanics)

Fund: 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).

Cite this article:

Liu Shi-Xing(刘世兴), Liu Chang(刘畅), and Guo Yong-Xin(郭永新) Geometric formulations and variational integrators of discrete autonomous Birkhoff systems 2011 Chin. Phys. B 20 034501

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