Generalized inertia in constrained body models (Q1080673)

The abstract concept of inertia as a functional, introduced by the author, ibid. 10, 1-7 (1983; Zbl 0511.70001) for simple body models, has proved useful in the formulation of the classical laws of motion in their various forms, and in particular in the form corresponding to the method of virtual work, which requires an inertial force system. In this note it is applied to bodies subject to holonomic constraints, which become a prototype of generalized body models. When generalized configurations, velocity fields and force systems are introduced, the generalized inertia may be defined, and the generalized inertial force systems derived from it (by a formula analogous to the one for simple body models) is shown to coincide with that obtained by transport from the original inertial force system. It is shown that, for a conservative system, the equations of motion reduce to Lagrange's equations.