Generalized co‐ordinate partitioning in static equilibrium analysis of large‐scale mechanical systems

This paper presents a computer‐based method for automatic formulation and efficient numerical solution of static equilibrium equations for nonlinear constrained mechanical systems with conservative forces. Nonlinear holonomic constraint equations and a potential energy function are written in terms of a maximal set of Cartesian generalized co‐ordinates. A stable static equilibrium configuration is found by minimizing the potential energy of the system, subject to the kinematic constraint equations, i.e. constrained optimization. A Gaussian elimination algorithm with full pivoting decomposes the constraint Jacobian matrix, identifies dependent and independent co‐ordinates and construct an influence coefficient matrix that relates variations in dependent and independent co‐ordinates. This information is employed to convert the constrained optimization problem to an unconstrained optimization problem. A simple example is presented to illustrate the method. An algorithm that may be used in analysis of large‐scale systems is presented.