中国物理B ›› 2016, Vol. 25 ›› Issue (11): 114501-114501.doi: 10.1088/1674-1056/25/11/114501

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇    下一篇

Generalized Birkhoffian representation of nonholonomic systems and its discrete variational algorithm

Shixing Liu(刘世兴), Chang Liu(刘畅), Wei Hua(花巍), Yongxin Guo(郭永新)   

  1. 1 College of Physics, Liaoning University, Shenyang 110036, China;
    2 College of Physics and Technology, Shenyang Normal University, Shenyang 110034, China;
    3 Eastern Liaoning University, Dandong 118001, China
  • 收稿日期:2016-04-30 修回日期:2016-06-03 出版日期:2016-11-05 发布日期:2016-11-05
  • 通讯作者: Chang Liu E-mail:liuchang101618@126.com
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11472124, 11572145, 11202090, and 11301350), the Doctor Research Start-up Fund of Liaoning Province, China (Grant No. 20141050), the China Postdoctoral Science Foundation (Grant No. 2014M560203), and the General Science and Technology Research Plans of Liaoning Educational Bureau, China (Grant No. L2013005).

Generalized Birkhoffian representation of nonholonomic systems and its discrete variational algorithm

Shixing Liu(刘世兴)1, Chang Liu(刘畅)1, Wei Hua(花巍)2, Yongxin Guo(郭永新)3   

  1. 1 College of Physics, Liaoning University, Shenyang 110036, China;
    2 College of Physics and Technology, Shenyang Normal University, Shenyang 110034, China;
    3 Eastern Liaoning University, Dandong 118001, China
  • Received:2016-04-30 Revised:2016-06-03 Online:2016-11-05 Published:2016-11-05
  • Contact: Chang Liu E-mail:liuchang101618@126.com
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11472124, 11572145, 11202090, and 11301350), the Doctor Research Start-up Fund of Liaoning Province, China (Grant No. 20141050), the China Postdoctoral Science Foundation (Grant No. 2014M560203), and the General Science and Technology Research Plans of Liaoning Educational Bureau, China (Grant No. L2013005).

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摘要： By using the discrete variational method, we study the numerical method of the general nonholonomic system in the generalized Birkhoffian framework, and construct a numerical method of generalized Birkhoffian equations called a self-adjoint-preserving algorithm. Numerical results show that it is reasonable to study the nonholonomic system by the structure-preserving algorithm in the generalized Birkhoffian framework.

关键词: nonholonomic system, generalized Birkhoffian system, conditions of self-adjointness, self-adjoint-preserving algorithm

Abstract: By using the discrete variational method, we study the numerical method of the general nonholonomic system in the generalized Birkhoffian framework, and construct a numerical method of generalized Birkhoffian equations called a self-adjoint-preserving algorithm. Numerical results show that it is reasonable to study the nonholonomic system by the structure-preserving algorithm in the generalized Birkhoffian framework.

Key words: nonholonomic system, generalized Birkhoffian system, conditions of self-adjointness, self-adjoint-preserving algorithm

中图分类号:  (Lagrangian and Hamiltonian mechanics)

  • 45.20.Jj
45.10.-b (Computational methods in classical mechanics)