论文标题
关于经典力学中Lagrange乘数方法的一致性
On the consistency of the Lagrange multiplier method in classical mechanics
论文作者
论文摘要
涉及滚动而不滑的问题或没有侧向滑动的问题，仅举几例，引入了速度依赖性约束，这些约束可以通过拉格朗日乘数方法在拉格朗日运动方程式中有效地治疗。这样一来，人们就发现，作为奖励，必须独立于运动方程的解决方案，并且只能取决于广义的坐标和速度以及时间。在本文中，我们确定了拉格朗日人应服从的条件，以确保可以始终获得约束力。
Problems involving rolling without slipping or no sideways skidding, to name a few, introduce velocity-dependent constraints that can be efficiently treated by the method of Lagrange multipliers in the Lagrangian formulation of the classical equations of motion. In doing so one finds, as a bonus, the constraint forces, which must be independent of the solution of the equations of motion, and can only depend on the generalized coordinates and velocities, as well as time. In this paper we establish the conditions the Lagrangian should obey that guarantee that the constraint forces can be obtained consistently.
