The Lie group Euler methods of multibody system dynamics with holonomic constraints

Abstract

The Euler methods on Lie group are developed for the differential-algebraic equations of multibody system dynamics with holonomic constraints. The implicit Euler method is used to solve the differential-algebraic equations as Euler-Lagrange equations on Lie group with indices 1, 2, and 3 and the case of overdetermined differential-algebraic equations mixing with configuration space. The symplectic Euler method is used to solve the differential-algebraic equations as constrained Hamilton equations on Lie group. For the discrete mapping between Lie group and Lie algebra, the canonical coordinates of the second kind for implicit first-order Crouch-Grossman Euler methods of differential-algebraic equations are used. A single pendulum and a double pendulum in the space are used to verify the accuracy of the Lie group Euler methods.

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