Dual Quaternion Variational Integrator for Rigid Body Dynamic Simulation

Abstract: We introduce a symplectic dual quaternion variational integrator(DQVI) for simulating single rigid body motion in all six degrees of freedom. Dual quaternion is used to represent rigid body kinematics and one-step Lie group variational integrator is used to conserve the geometric structure, energy and momentum of the system during the simulation. The combination of these two becomes the first Lie group variational integrator for rigid body simulation without decoupling translations and rotations. Newton-Raphson method is used to solve the recursive dynamic equation. This method is suitable for real-time rigid body simulations with high precision under large time step. DQVI respects the symplectic structure of the system with excellent long-term conservation of geometry structure, momentum and energy. It also allows the reference point and 6-by-6 inertia matrix to be arbitrarily defined, which is very convenient for a variety of engineering problems.