A State–Space Based Implicit Integration Algorithm for Differential–Algebraic Equations of Multibody Dynamics

An implicit numerical integration algorithm based on generalized coordinate partitioning is presented for the numerical solution of differential–algebraic equations of motion arising in multibody dynamics. The algorithm employs implicit numerical integration formulas to express independent generalized coordinates and their first time derivative as functions of independent accelerations at discrete integration times. The latter are determined as the solution of discretized equations obtained from state–space, second order ordinary differential equations in the independent coordinates. All dependent variables in the formulation, including Lagrange multipliers, are determined by satisfying the full system of kinematic and kinetic equations of motion. The algorithm is illustrated using the implicit trapezoidal rule to integrate the constrained equations of motion for three stiff mechanical systems with different generalized coordinate dimensions. Results show that the algorithm is robust and has the capability to integrate differential–algebraic equations of motion for stiff multibody dynamic systems. __________________________ Department of Mechanical Engineering, The University of Iowa, Iowa City, IA 52242 Department of Mathematics, The University of Iowa, Iowa City, IA 52242