非线性约束动力学系统的Lagrange逆问题

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。

Lagrangian Inverse Problem of Nonlinear Constrained Dynamical Systems

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.