Geometric concept of isokinetic constraint for a system of particles

Abstract

The paper deals with the geometric concept of mechanical systems of N particles. The systems are modelled on the Cartesian product R ¢ X N and its first jet prolongation J 1 .R ¢ X N / h R ¢ T X N , where X is a 3-dimensional Riemannian manifold with a metric G. The kinetic energy T of the system of N-particles is interpreted by means of the weighted quadratic form x Q G associated with the weighted metric tensor G which arises from the original metric tensor G and the system of N particles m 1 ; : : : ; m N. A requirement for the kinetic energy of the system of N particles to be constant is regarded as a nonholonomic, so-called isokinetic constraint and it is defined as a fibered submanifold T of the jet space R ¢ T X N endowed with a certain distribution C called canonical distribution, which has the meaning of generalized admissible displacements of the system of particles subject to the isokinetic constraint. Vector generators of the canonical distribution are found.

Higher Order Hamiltonian Systems with Generalized Legendre Transformation

“…This approach is not well adapted to study Lagrangians that are singular in the standard sense. Note that an alternative approach to the study of "degenerated" Lagrangians (singular in the standard sense) is the constraint theory from mechanics (see [19,20]) and in the field theory [21].…”