chapter  5
52 Pages

Particle on a Curve and on a Surface

WithJohn G. Papastavridis

In this chapter, using the hitherto developed tensorial machinery, and since analytical dynamics (AD) models the motions of the most general mechanical systems as motions of a single fictitious, or figurative, particle in configuration space (Section 4.2), we begin our study of mechanics by discussing the dynamics of a particle in ordinary three-dimensional Euclidean (flat) space E3 : in general and in intrinsic variables; on a general space, or skew, or twisted, curve; and on a general curved surface lying there. Then, we extend these results to n-dimensional (Riemannian) surfaces and, finally, discuss the theory of perturbation of (actual or figurative) particle trajectories in configuration space, and their stability.*