Hagedorn's theorem in some special cases of rheonomic systems

摘要

Hagedorn's theorem on instability [Arch. Rational Mech. Anal. 58 (1976) 1], deduced from Jacobi's form of Hamilton's principle, refers to seleronomic mechanical systems. In this paper we shall prove that Hagedorn's methodology can be generalized to a class of rheonomic mechanical systems with differential equations of motion which allow the existence of Painleve's integral of energy. The application of this methodology to the case of rheonomic systems which allow, together with Painleve's integral, cyclic integrals, as well as to the mechanical systems having resultant motion, with prescribed transport motion, and, finally, to the systems having Mayer's rheonomic potential, are also considered. Obtained results are illustrated by an example. (c) 2004 Elsevier Ltd. All rights reserved.