On the Modeling of Dynamic Systems

In this paper, several dynamic systems are modeled using the time domain finite element method. Galerkins' Weak Principle is used to model the general second-order mechanical system, and is applied to a simple pendulum dynamics. Problems caused by approximating the final momentum are also investigated. Extending the research, some dynamic analysis methods are suggested for the hybrid coordinate systems that have both slew and flexible modes. The proposed methods are based on both Extended Hamilton's Principle and Galerkin's Weak Principle. The matrix wave equation is propagated in space domain, satisfying the geometric/natural boundary conditions. As a result, the flexible motion can be obtained compatible with the applied control input. Numerical example is shown to demonstrate the effectiveness of the proposed modeling methods for the hybrid coordinate systems.