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 conditions the Lagrangian and the constraints should obey in order to guarantee that the constraint forces can be obtained consistently.

中文翻译：

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论经典力学中拉格朗日乘子法的一致性

涉及滚动而不打滑或没有侧向打滑的问题，仅举几例，引入了与速度相关的约束，可以通过经典运动方程的拉格朗日公式中的拉格朗日乘子方法有效地处理这些约束。在这样做时，作为奖励，人们发现约束力必须独立于运动方程的解，并且只能依赖于广义坐标和速度以及时间。在本文中，我们建立了拉格朗日函数和约束应遵守的条件，以保证约束力可以一致地获得。