Differential geometric aspects of dynamics

The relations between mathematics and physics have been presented so frequently and so adequately in recent years, that further discussion would seem unnecessary. Mathematics, however, is too often taken to be analysis, and the role of geom- etry is neglected. Geometry may be viewed either as a branch of pure mathematics, or as the simplest of the physical sciences. For our discussion we choose the latter point of view: geometry is the science of actual physical or intuitive space. All physical phenomena take place in space, and hence necessarily present geometric aspects. We confine our discussion to mechanics, and consider the r61e of geometry in mechanics.