General Formulation of the Mechanics of Point Particles

Abstract

The second axiom of Newton implies, that the time development of the motion of a point particle or a system of point particles can be calculated, if the forces acting on the particle are known. Besides the fact that the solution of the equations of motion is not necessarily a simple matter, difficulties can arise from different quarters. It is possible that the forces (in the form of a force field or as a function of time or …) are not known explicitly. The motion can be restricted by constraints, which are expressed in the form of geometrical conditions. A simple example of this kind of restriction is the motion on an inclined plane. The pressure, which an object (a mass point) exerts on the surface of the plane, generates a counter pressure which compensates in part the effect of gravitation. This constraining force can be determined by simple means in the case of the inclined plane.