Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (1): 68-72.

• Articles • Previous Articles     Next Articles

POINCARÉ-CARTAN INTEGRAL INVARIANTS OF BIRKHOFFIAN SYSTEMS

GUO Yong-xin1, SHANG Mei2, LUO Shao-kai3   

  1. 1. Department of Physics, Liaoning University, Shenyang 110036, China;
    2. Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China;
    3. Institute of Mathematical Mechanics and Mathematical Physics, Changsha University, Changsha 410003, China
  • Received:2001-02-10 Revised:2002-07-30 Online:2003-01-18 Published:2003-01-18
  • Supported by:

    the National Natural Science Foundation of China(10175032);the Natural Science Foundation of Liaoning Province of China(002083);the Natural Science Foundation of Henan Province of China(998040080);the Science Research Foundation of Liaoning Educational Committee of China(990111004,20021004)

Abstract: Based on modern differential geometry, the symplectic structure of a Birkhoffian system which is an extension of conservative and nonconservative systems is analyzed. An integral invariant of Poincaré-Cartan’s type is constructed for Birkhoffian systems. Finally, one-dimensional damped vibration is taken as an illustrative example and an integral invariant of Poincaré’s type is found.

2010 MSC Number: 

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