Dual Quaternion Variational Integrator for Rigid Body Dynamic Simulation

Abstract

In rigid body dynamic simulations, often the algorithm is required to deal with general situations where both reference point and inertia matrix are arbitrarily de- fined. We introduce a novel Lie group variational integrator using dual quaternion for simulating rigid body dynamics in all six degrees of freedom. Dual quaternion is used to represent rigid body kinematics and one-step Lie group method is used to derive dynamic equations. The combination of these two becomes the first Lie group variational integrator for rigid body dynamics without decoupling translations and rotations. Newton-Raphson method is used to solve the recursive dynamic equation. Our method is suitable for rigid body simulations with high accuracy under large time step. The entire dynamics-control system can now be established based on dual quaternions without re-projection from Cartesian frame. A numerical example of spacecraft-cargo separation process proves that our method respects the symplectic structure of the system with excellent long-term conservation of geometry structure, momentum and energy. In instants where separation happens, reference point transformation is no longer required.