非线性约束下非完整系统的平衡稳定性

V·柯维克; M·维什柯维克; D·狄加瑞克; A·阿伯拉达维克

doi:10.3879/j.issn.1000-0887.2010.06.009

非线性约束下非完整系统的平衡稳定性

doi: 10.3879/j.issn.1000-0887.2010.06.009

贝尔格莱德大学机械工程学院,11120 贝尔格莱德,塞尔维亚;2.克拉克耶瓦茨大学机械工程学院,36000 克拉列沃,塞尔维亚

基金项目: 塞尔维亚共和国科学部技术局资助项目(144019;114052)

详细信息

中图分类号: O175.13；O316
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出版历程
- 收稿日期: 2009-12-14
- 修回日期: 2010-03-04
- 刊出日期: 2010-06-15

On the Stability of Equilibria of Nonholonomic Systems With Nonlinear Constraints

University of Belgrade, Faculty of Mechanical Engineering, Kraljice Marije 16, 11120 Belgrade, Serbia;

摘要

摘要: Kozlov将Liapunov第一方法推广到非线性力学系统，用来解决保守和耗散力场中，运动力学系统平衡位置的不稳定性．文中讨论的系统运动限于理想的非线性非完整约束．将势能和约束函数展开为Maclaurin级数，对其第一非平凡多项式的阶，确定了相互间关系的5种情况，并对生成的非线性非完整约束方程进行了分析．将3种线性齐次约束下的非完整系统平衡位置的不稳定定理(Kozlov,1986)，推广到非线性非完整约束．另外两种情况下的新定理，也是将Kozlov(1994)的结果，拓展到非线性约束下的非完整系统．
- Liapunov第一方法 /
- 非完整系统 /
- 平衡的不稳定性
Abstract: Liapunov's first method, extended by Kozlov to non linearm echanical systems, was applied to the study of the in stability of the position of equilibrium of amechanical system moving in the field of conservative and dissipative forces. The motion of the system was lmiited by ideal nonlinear nonholonomic constraints. Five cases determined by the relationship between the degree of the first non trivial polynomials in Maclaurin's series for the potential energy and the functions that can be generated from the equations of non linear nonholonomic constraints were analyzed. In the three cases the theoremon the instability of the position of equilibrium of non holonomic systems with linear homogeneous constraints (Kozlov (1986)) was generalized to the case of non linear nonhom ogeneous constraints. In the other two cases new theorems were setextending the result from Kozlov (1994) to nonholonomic systems with non linear constraints.
- Liapunov first method /
- nonholonomic system /
- in stability of equilibrium

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参考文献(12)

[1]	Dobronravov V V. Foundations of the Mechanics of Nonholonomic Systems[M]. Moscow: Vysshaya Shkola,1971:247. (in Russian)
[2]	Kozlov V V, Palamodov V P. On asymptotic solutions of the equations of classical mechanics[J]. Soviet Math Dokl, 1982, 263(2): 285-289. (in Russian)
[3]	Kozlov V V. On the stability of equilibria of non-holonomic systems[J]. Soviet Math Dokl, 1986, 33(3): 654-656.
[4]	Kozlov V V. Asymptotic motions and inversion of the Lagrange-Dirichlet theorem[J]. J Appl Maths Mechs,1986, 50(6): 719-725. doi: 10.1016/0021-8928(86)90079-1
[5]	Kozlov V V. On the asymptotic motions of systems with dissipation[J]. J Appl Maths Mechs, 1994, 58(5): 787-792. doi: 10.1016/0021-8928(94)90003-5
[6]	Kozlov V V, Furta S D. Lyapunov’s first method for strongly non-linear systems[J]. Resenhas IME-USP, 2001, 5(1):1-24.
[7]	Furta S D. On asymptotic solutions of equations of motion of mechanical systems[J]. J Appl Maths Mechs,1986, 50(6): 938-944.
[8]	Lyapunov A M. The General Problem of the Stability of Motion[M]. Khar’kov: Khar’kov Mat Obshch, 1892:450. (in Russian)
[9]	Kuznetsov A N. The existence of solutions of an autonomous system, recurring at a singular point, having a formal solution[J]. Funktsional’nyi Analiz i Yego Prilozheniya,1989, 23(4): 63-74. (in Russian)
[10]	Hagedorn P. Die umkehrung der stabilitātssātze von Lagrange—dirichlet und routh[J]. Arch Rational Mech Anal, 1971, 42(4): 281-316.
[11]	Cˇovic＇ V, Veskovic＇ M. Hagedorn’s theorem in some special cases of rheonomic systems[J]. Mechanics Research Communications, 2005, 32(3): 265-280. doi: 10.1016/j.mechrescom.2004.02.009
[12]	Veskovic＇ M, Cˇovic＇ V. Lyapunov first method for nonholonomic systems with circulatory forces[J]. Mathematical and Computer Modeling, 2007, 45(9/10): 1145-1156. doi: 10.1016/j.mcm.2006.09.015