一类高阶非完整约束Chetaev原理的推广
A Generalization of Chetaev's Principle for a Class of Higher Order Non-holonomic Constraints
摘要：
约束分布在非完整力学中具有双重作用。一方面，它是一种运动学约束，即对运动本身的约束。另一方面，它也是在使用达朗贝尔原理推导运动方程时对允许变化的限制。我们将表明，许多系统的物理利益，达朗贝尔原理不适用，可以方便地模拟虚功原理的一般思想，通过引入运动学约束和变分约束作为独立的实体。这包括例如弹性滚动体和充气轮胎。此外，达朗贝尔原理和切塔耶夫原理也属于这个方案。我们强调几何的观点，避免使用局部坐标，这是处理全球性问题的适当设置，如减少。
英文摘要：
The constraint distribution in non-holonomic mechanics has a double role. On one hand, it is a kinematic constraint, that is, it is a restriction on the motion itself. On the other hand, it is also a restriction on the allowed variations when using D'Alembert's Principle to derive the equations of motion. We will show that many systems of physical interest where D'Alembert's Principle does not apply can be conveniently modeled within the general idea of the Principle of Virtual Work by the introduction of both kinematic constraints and variational constraints as being independent entities. This includes, for example, elastic rolling bodies and pneumatic tires. Also, D'Alembert's Principle and Chetaev's Principle fall into this scheme. We emphasize the geometric point of view, avoiding the use of local coordinates, which is the appropriate setting for dealing with questions of global nature, like reduction.
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