The Impulsive Action Integral for Rigid-Body Mechanical Systems With Impacts

Abstract

There is a missing link in analytical mechanics which shows that general impactive processes are obtained by extremizing some sort of action integral for which momentum and energy are not necessarily conserved. In this work, the conditions under which general nonconserving impacts become a part of an extremizing solution for mechanical systems, which are scleronomic (not explicitly time depending) and holonomic, are investigated. The stationarity conditions of an impulsive action integral are investigated and the main theorem is proven. The general momentum balance and the total energy change over a collisional impact for a mechanical scleronomic holonomic finite-dimensional Lagrangian system are obtained in the form of stationarity conditions of a modified action integral under a regularity condition on the impactive transition sets.