Mechanical systems with nonholonomic constraints
Mechanical systems with nonholonomic constraints
复制标题
具有非完整约束的机械系统
DOI：
10.1063/1.532196
复制
发表时间：
1997
期刊：
影响因子：
--
通讯作者：
O. Krupkova
中科院分区：
文献类型：
--
作者：
O. Krupkova
本文给出了一般非完整约束一阶力学系统理论的几何框架。所考虑的力学系统不应该是拉格朗日系统，并且约束不应该是速度的特殊形式（例如，仿射或线性）。一个力学系统在纤维流形的第一个喷注延拓上有一个2-形式的等价类。非完整约束被定义为第一喷流延伸的子流形。它表明，这个子流形是典型地赋予一个分布，这个分布（分别，其垂直子分布）具有广义可能的含义（分别，虚拟）位移。定义了约束力的概念，提出了虚功原理的几何形式。从虚功原理出发，导出了无功约束力的计算公式。一个机械系统的非完整约束建模为…
A geometric setting for the theory of first-order mechanical systems subject to general nonholonomic constraints is presented. Mechanical systems under consideration are not supposed to be Lagrangian systems, and the constraints are not supposed to be of a special form in the velocities (as, e.g., affine or linear). A mechanical system is characterized by a certain equivalence class of 2-forms on the first jet prolongation of a fibered manifold. The nonholonomic constraints are defined to be a submanifold of the first jet prolongation. It is shown that this submanifold is canonically endowed with a distribution—this distribution (resp., its vertical subdistribution) has the meaning of generalized possible (resp., virtual) displacements. The concept of a constraint force is defined, and a geometric version of the principle of virtual work is proposed. From the principle of virtual work a formula for a workless constraint force is obtained. A mechanical system subject nonholonomic constraints is modeled as ...