N-Particle Systems

Abstract

Newton’s first and second laws really refer only to particles, for they make no reference to properties like size, elasticity, and internal angular momentum. The objects described by these laws have only mass and position. The properties of extended objects must be included in the theory by a process of summation or integration. In physics generally there are two situations of special interest: where the bodies are few in number, say up to 4 or 5, and where there are about 10²³ of them. The situations are very different, starting with the kind of question one wishes to ask — macroscopic quantities like pressure, temperature and density have no counterparts in a few-body system. If one is thinking about a rigid solid one must decide what rigidity means; if the solid is elastic there are assumptions to be made concerning the nature of its elasticity. In Sect. 4.6 an elementary calculation in hydrodynamics will require four assumptions in addition to the assumption that a small element of the fluid obeys Newton’s second law. Except for Sects. 4.5 and 4.6 this chapter will be concerned with the simplest cases, in which the N particles can be considered one at a time, each one obeying Newton’s laws. Rigid and elastic bodies will be discussed in Chaps. 8 and 9.