| 非线性约束动力学系统的Lagrange逆问题 |
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| 引用本文： | 白文君,于莹. 非线性约束动力学系统的Lagrange逆问题[J]. 辽宁大学学报(自然科学版), 2000, 27(2): 118-122 |
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| 作者姓名： | 白文君 于莹 |
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| 作者单位： | 1. 沈阳教育学院,物理系,辽宁,沈阳,110015
2. 沈阳工业大学,数理系,辽宁,沈阳,110023 |
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| 摘 要： | 通常处理带约束的Ｌａｇｒａｎｇｅ逆问题和稳定作用量原理都局限于一类特殊的线性约束动力学系统，即Ｃｈａｐｌｙｇｉｎ系统，本文运用现代微分几何方法证明了当一般约束动力学系统的对称性满足一定条件时，也同样存在拉氏量，因而这类系统的动力学方程可由稳定作用量原理导出。
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| 关 键 词： | 非线笥约束动力学系统 C系统 Lagrange逆问题 |
Lagrangian Inverse Problem of Nonlinear Constrained Dynamical Systems |
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| BAI Wenjun,YU Ying. Lagrangian Inverse Problem of Nonlinear Constrained Dynamical Systems[J]. Journal of Liaoning University(Natural Sciences Edition), 2000, 27(2): 118-122 |
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| Authors: | BAI Wenjun YU Ying |
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| Abstract: | Traditionally the treatment of Lagrangian inverse problem and stationary variational principle in the presence of constraints are restricted to a special kind of linear constrained dynamical systems, i.e.,Chaplygin's systems. In this paper we prove in terms of modern differential geometry that there exist Lagrangians for general constrained dynamical systems if the adjoint symmetries of the systems satisfy certain conditions. As a result the dynamical equations of the systems can be derived from a stationary action principle. |
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| Keywords: | non holonomic constraints Chaplygin's systems adjoint symmetries Lagrangian inverse problem. |
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