Dynamics II: Problems of Motion

Abstract

Newton’s equations of motion allow, at least in principle, the calculation of the time development of a system of mass points. The prerequisite is that all forces of the system (e.g. as functions of the position of the particles) and the initial conditions for all masses are known. Independent of the technical realisation of such calculations, a distinction is necessary between integrable or chaotic systems. This point will be addressed in Chap. 5.4.3. A system is called integrable if initial conditions that are infinitesimally close will lead to solutions that are infinitesimal close. The solution diverges (exponentially) even for infinitesimally close initial conditions in the case of chaotic systems.