Holonomic Point Mass Systems

The motion of a mechanical system is generally geometrically restricted by constraints. The constraints define the free spatial directions in which the motion of the system takes place, and the orthogonal, blocked spatial directions, in which constraint forces are transmitted. In this chapter, the formulations of the equations of motion for constrained point mass systems are developed. Starting from a classification of constraints, holonomic constraints are formulated in implicit and explicit representations. For the point masses, the linear momentum laws apply with the applied forces and the constraint forces. The lines of action of the constraint forces are defined by the constraints according to the principles of d’Alembert-Lagrange or Jourdain. From this, two formulations of the equations of motion are developed: Differential-algebraic equations in the interdependent absolute coordinates of the point masses and ordinary differential equations in independent minimal coordinates.