二阶类摆系统的临界阻尼

基金项目: 国家自然科学基金资助项目(10272001;60334030);国家重点基础研究专项经费资助项目(G20000773)

Critical Damping of the Second-Order Pendulum-Like Systems

1.
Department of Mechanics and Engineering Science, Peking Univeristy, Beijing 100871, P. R. China;

摘要: 首先，分析了一具有特定非线性函数的二阶类摆系统的解的性质；进而，针对具有一般非线性形式的二阶类摆系统，利用微分方程的定性分析方法讨论了其总体性质，并由此给出了估算其临界阻尼的充分性条件．改进了Leonov等人的工作．
- 类摆系统 /
- Lagrange稳定 /
- 类梯度 /
- 第二类极限环
Abstract: First,the properties of solutions of a typical second-order pendulum-like system with a specified nonlinear function were dicussed.Then the case with a general form of nonlinearity is considered and its global properties were studied by using the qualitative theory of differential equations.As a result,sufficient conditions for estimating the critical damp are established,which improves the work by Leonov et al.
- pendulum-like system /
- Lagrange stability /
- gradient-like behavior /
- limit cycles of the second kind

[1]	Leonov G A,Smirnova V B. Analysis of frequency-of-oscillations-controlled systems[A].In:St Petersbuvg,Ed.Proceedings of International Conference on Control of Oscillations and Chaos[C](Russia).1997,2:439—441.
[2]	Leonov G A,Tomayev A,Chshiyeva T.Stability of frequency-phase locked automatic frequency control systems[J].Soviet Journal of Communications Technology and Electronics,1992,37(11):1—9.
[3]	Tricomi F. Integrazione di unequazione differenziale presentatasi in electrotechnica[J].Annali Della Roma Scuola Normale Superiore de Pisa:Scienza Phys e Mat,1933,2:1—20.
[4]	Andronow A A,Chaikin C E.Theory of Oscillations[M].Princeton University Press, 1966.
[5]	Amerio L. Determinazione delle condizioni di stabilita per gli integrali di un'equazione ineressante I'elettrotacnica[J].Annali di Matematica Pura ed Applicata,1949,4(30):75—90.
[6]	Hayes W D. On the equation for a damped pendulum under constant torque[J].Z A M Ph,1953,4(5):398—401. doi: 10.1007/BF02074983
[7]	Sansone G,Conti R.非线性微分方程[M].黄启昌，金成桴，史希福译. 北京：科学出版社，1983.
[8]	Leonov G A,Ponomarenko D V,Smirnova V B.Frequency-Domain Methods for Nonlinear Analysis[M].Singapore: World Scientific, 1996.
[9]	Arie E,Botgros M,Halanay A,et al.Transient stability of the synchronous machine[J].Rev Roum Sci Techn Serie Electrotechn et Energy,1974,19(4):611—625.