Stabilized Explicit Integrators for Local Parametrization in Multi-Rigid-Body System Dynamics

Abstract

In this work, stabilized explicit integrators for local parametrization are introduced to calculate the dynamics of constrained multi-rigid-body systems, including those based on the orthogonal Runge–Kutta–Chebyshev (RKC) method and the extrapolated stabilized explicit Runge–Kutta (ESERK) method. Both of these methods have large stability regions at the negative real axis, and this property makes them suitable to settle the introduction of the stabilization parameter for a constraint equation. The local vectorial rotation parameters are adopted to describe rotations in each rigid body, and a stabilization technique is developed to transform the differential-algebraic equations (DAE) into a set of first-order ordinary differential equations (ODEs) that can be computed efficiently. Several benchmarks are calculated and the results are compared to those by the generalized-α integrator and ADAMS models, verifying their effectiveness in nonstiff problems.