Free motion and initial motion of controllable holonomic system with redundant coordinates

When the parameters of a system are not completely independent, it is called a holonomic system with redundant coordinates. This article explored the free motion and initial motion of a controllable holonomic system with redundant coordinates. Firstly, the differential equations of motion were established according to the d'Alembert-Lagrange principle, and the multipliers of constraints were obtained. Secondly, according to the definition of free motion of a constrained system, all the multipliers were set to zero, and the conditions for free motion of the system were obtained. Thirdly, the initial motion of the system was studied, when the initial condition of motion and control parameters were given. Finally, an example was given to illustrate the application of this method.