Dynamic response of mechanical systems by a weak Hamiltonian formulation

Abstract

The paper explains the appropriate use of Hamilton's Weak Principle (HWP) in the developement of consistent and efficient approximations for the determination of the response of mechanical systems. In particular it is shown how the HWP can be used to provide explicit and implicit integration formulae and to study the response and stability of nonlinear periodic systems. The discussion of the stability of the integration formula is also included. Some numerical examples show the result that can be obtained when the HWP is applied to some simple but significant response problems.