ABSTRACT
The dynamic systems we have discussed up to this point have their number of degrees of freedom finite, and they are hence countable. There are some mechanical problems, however, which involve continuous systems as, for example, the problem of a vibrating elastic solid. Here, each point of the continuous solid partakes in the oscillations, and the complete motion can only be described by specifying the position coordinates of all points. The coordinates and momenta of discrete mechanics are replaced by field quantities, that is, functions or fields defined over space and time, which describe the dynamics of the system. It is not difficult to modify the previous formulations of discrete mechanics so as to handle such problems. The most direct method is to approximate the continuous system by one containing discrete particles and then examine the change in the equations describing the motion as the continuous limit is approached.
