NUMERICAL INTEGRATION OF CONSTRAINED MULTI-BODY DYNAMICAL SYSTEMS USING 5TH ORDER EXACT ANALYTIC CONTINUATION ALGORITHM

摘要

Many numerical integration methods have been developed for predicting thernevolution of the response of dynamical systems. Standard algorithms approachrnapproximate the solution at a future time by introducing using a truncatedrnpower series representation that attempts to recover an n-th order Taylor seriesrnapproximation, while only numerically sampling a single derivative model. Anrnexact fifth-order analytic continuation method is presented for integrating constrainedrnmultibody vector-valued systems of equations, where the Jacobi formrnof the Routh-Voss equations of motion simultaneously generates the accelerationrnand Lagrange multiplier solution. The constraint drift problem is addressedrnby introducing an analytic continuation method that rigorously enforces the kinematicrnconstraints through five time derivatives. The proposed approach isrnexpected to be particularly useful for stiff dynamical systems, as well as systemsrnwhere implicit integration formulations are introduced. Numerical examplesrnare presented that demonstrate the effectiveness of the proposed methodology.