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Chin. Phys. B, 2014, Vol. 23(6): 064501    DOI: 10.1088/1674-1056/23/6/064501
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next  

Research on the discrete variational method for a Birkhoffian system

Liu Shi-Xinga, Hua Weib, Guo Yong-Xina
a College of Physics, Liaoning University, Shenyang 110036, China;
b College of Physics and Technology, Shenyang Normal University, Shenyang 110034, China
Abstract  In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structures of Birkhoffian systems. A numerical experiment for a damping oscillator system is conducted. The result shows that the new algorithm can better simulate the energy dissipation than the R-K method, which illustrates that we can numerically solve the dynamical equations by the discrete variational method in a Birkhoffian framework for the systems with a general symplectic structure. Furthermore, it is demonstrated that the results of the numerical experiments are determined not by the constructing methods of Birkhoffian functions but by whether the numerical method can preserve the inherent nature of the dynamical system.
Keywords:  Birkhoff's equations      discrete variational methods      general symplectic structure      discrete Birkhoff's equations  
Received:  25 June 2013      Revised:  10 November 2013      Published:  15 June 2014
PACS:  45.20.Jj (Lagrangian and Hamiltonian mechanics)  
  45.10.-b (Computational methods in classical mechanics)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11301350, 11172120, and 11202090) and the Liaoning University Pre-reporting Fund Natural Projects (Grant No. 2013LDGY02).
Corresponding Authors:  Guo Yong-Xin     E-mail:  yxguo@lnu.edu.cn

Cite this article: 

Liu Shi-Xing, Hua Wei, Guo Yong-Xin Research on the discrete variational method for a Birkhoffian system 2014 Chin. Phys. B 23 064501

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