An Analytic Continuation Method to Integrate Constrained Multi-Body Dynamical Systems

Many numerical integration methods have been developed for predicting the evolution of the response of dynamical systems. Standard algorithms approach approximate the solution at a future time by introducing a truncated power series representation that attempts to recover an n-th order Taylor series approximation, while only numerically sampling a single derivative model. This work presents an exact fifth-order analytic continuation method for integrating constrained multi-body vector-valued systems of equations, where the Jacobi form of the Routh-Voss equations of motion simultaneously generates the acceleration and Lagrange multiplier solution. The constraint drift problem is addressed by introducing an analytic continuation method that rigorously enforces the kinematic constraints through five time derivatives. This work rigorously deals with the problem of handling the time-varying matrix equations that characterize real-world equation of motion models arising in science and engineering. The proposed approach is expected to be particularly useful for stiff dynamical systems, as well as systems where implicit integration formulations are introduced. Numerical examples are presented that demonstrate the effectiveness of the proposed methodology.