ABSTRACT
In the following section it will be shown that all reversible mechanical systems can be described in terms of a simple principle known, rather obscurely, as the 'principle of least action'. Before moving on to this, it is worthwhile reviewing the concepts of generalized coordinates. First, consider a system of N infinitesimally small particles, the position of each can be determined in rectangular, or Cartesian, coordinates from the values
x,,y,,z, i = 1, 2, ... N (3.1)
(3.2)
For example, for a single particle, it might be more desirable to use spherical coordinates. The relationship between the two systems is given by
m2 Figure 3.1: Two rigid point masses connected by a rigid massless link of length a
constraint such that
(3.3)
(3.4)
For a system of free particles 3N is the number of degrees of freedom. Clearly, to control the motion of a mechanical system, there must be some constraints. Consider an idealized molecule made up from two rigidly connected atoms a fixed distance a apart, figure 3.1.
