A Formulation and Interpretation of Equation of Motion in Energy Momentum Method

Abstract

Numerical solution of Lagrange equation of motion for geometrically nonlinear rigid and flexible body dynamics has essentially a risk for numerical instability associated with time integration : There have been proposed several methods including energy momentum method that avoid this instability by enforcing the conservation of total energy and momentum.The energy momentum method provides a modification of the Lagrange equation of motion to ensure the solution satisfies the conservation unconditionally. However, there is few literatures that explain the detail on the relation between the original Lagrange equation and the modified equation of motion. This paper presents the straightforward derivation of the modified equation from the conservation principle of the energy and momentum. The general condition to formulate the energy momentum conservation algorithm in also shown in this derivation process. The results clarify the physical meanings of each term in the modified equation of motion.