Equations of Motion for Structures in Terms of Quasi-Coordinates

Abstract

A form of Lagrange’s equations in terms of quasi-coordinates (Boltzmann/Hamel equations) is presented. Identities are introduced which permit a straightforward method for formulating the equations of motion for structures for which the kinetic and potential energies are explicit functions of angular orientation. This formulation may be utilized once the energies are expressed in matrix form as functions of angular velocities and coordinate transformation matrices. This method is particularly useful for a large class of problems in the dynamics of structures including spacecraft, robots, ground vehicles, and aircraft.