Abstract
Abstract
Numerical solution of the Lagrange equation of motion for geometrically non-linear rigid and flexible dynamics essentially has a risk of numerical instability associated with time integration. Several methods have been proposed, including the energy-momentum method (EMM), that avoid this instability by enforcing the conservation of total energy and momentum. The EMM provides equations of motion that are modified from the d'Alembert-Lagrange equations, ensuring that the solution satisfies the conservation unconditionally. However, there are few studies in the literature that explain the detail of the relationship between the original d'Alembert-Lagrange equations and the modified equations of motion. This paper examines the direct derivation of modified equations of motion from the conservation principles of energy and momentum. The general condition for formulation of the energy momentum conservation algorithm is also shown in this derivation process. The result clarifies the physical meaning of each term in the modified equation of motion.
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