中国物理B ›› 2008, Vol. 17 ›› Issue (11): 3942-3952.doi: 10.1088/1674-1056/17/11/004

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Symplectic-energy-first integrators of discrete mechanico-electrical dynamical systems

付 昊1, 陈本永2, 傅景礼3, 唐贻发4   

  1. (1)China Jingye Engineering Corporation Limited, Shenzhen Brach, Shenzhen 518054, China; (2)Faculty of Mechanical-Engineering $\&$ Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China; (3)Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; (4)State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences，Beijing 100080, China
  • 收稿日期:2008-02-06 修回日期:2008-04-08 出版日期:2008-11-20 发布日期:2008-11-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10672143 and 60575055) and the State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences and the Natural Science Foundation of Henan Province Government, China (Grant No 0511022200).

Symplectic-energy-first integrators of discrete mechanico-electrical dynamical systems

Fu Jing-Li(傅景礼)a, Chen Ben-Yong (陈本永)b, Tang Yi-Fa(唐贻发)c,  Fu Hao (付昊)d   

  1. a Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; b Faculty of Mechanical-Engineering $\&$ Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China; c State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences，Beijing 100080, China; d China Jingye Engineering Corporation Limited, Shenzhen Brach, Shenzhen 518054, China
  • Received:2008-02-06 Revised:2008-04-08 Online:2008-11-20 Published:2008-11-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10672143 and 60575055) and the State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences and the Natural Science Foundation of Henan Province Government, China (Grant No 0511022200).

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摘要： A discrete total variation calculus with variable time steps is presented for mechanico-electrical systems where there exist non-potential and dissipative forces. By using this discrete variation calculus, the symplectic-energy-first integrators for mechanico-electrical systems are derived. To do this, the time step adaptation is employed. The discrete variational principle and the Euler--Lagrange equation are derived for the systems. By using this discrete algorithm it is shown that mechanico-electrical systems are not symplectic and their energies are not conserved unless they are Lagrange mechanico-electrical systems. A practical example is presented to illustrate these results.

关键词: total variation, symplectic-energy--momentum integrator, mechanico-electrical system

Abstract: A discrete total variation calculus with variable time steps is presented for mechanico-electrical systems where there exist non-potential and dissipative forces. By using this discrete variation calculus, the symplectic-energy-first integrators for mechanico-electrical systems are derived. To do this, the time step adaptation is employed. The discrete variational principle and the Euler--Lagrange equation are derived for the systems. By using this discrete algorithm it is shown that mechanico-electrical systems are not symplectic and their energies are not conserved unless they are Lagrange mechanico-electrical systems. A practical example is presented to illustrate these results.

Key words: total variation, symplectic-energy--momentum integrator, mechanico-electrical system

中图分类号:  (Circuit theory)

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