Derivation of the equations of motion for complex structures by symbolic manipulation

Abstract

This paper outlines a computer program especially tailored to the task of deriving explicit equations of motion for structures with point-connected substructures. The special purpose program is written in FORTRAN and is designed for performing the specific algebraic operations encountered in the derivation of explicit equations of motion. The derivation is by the Lagrangian approach. Using an orderly kinematical procedure and a discretization and/or truncation scheme, it is possible to write the kinetic and potential energy of each substructure in a compact vector-matrix form. Then, if each element of the matrices and vectors encountered in the kinetic and potential energy is a known algebraic expression, the computer program performs the necessary operations to evaluate the kinetic and potential energy of the system explicitly. Lagrange's equations for small motions about equilibrium can be deduced directly from the explicit form of the system kinetic and potential energy.