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

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