Generalized Coordinate Partitioning Methods for Numerical Integration of Differential-Algebraic Equations of Dynamics
Explicit and implicit, stiffly stable numerical integration algorithms based on generalized coordinate partitioning are developed and demonstrated for automated simulation of multibody dynamic systems. The concept of generalized coordinate partitioning is used to parameterize the constraint set with independent generalized coordinates. A stiffly stable, backward differentiation formulas are applied to determine independent generalized coordinates and velocities. Dependent generalized coordinates, velocities, and accelerations, as well as Lagrange multipliers that account for constraints, are explicitly retained in the formulation to satisfy all of the governing kinematic and dynamic equations. The algorithm is shown to be valid and accurate, both theoretically and through solution of a numerical example.
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