Dual Quaternions Representation of Lagrange's Dynamic Equations

Abstract

Abstract This paper introduces for the first time, the Lagrange's dynamic equations in dual number quaternion form. Additionally, Rayleigh's dissipation function in dual quaternion form is introduced here allowing for the accounting of dissipative (non-conservative) forces such as motion through a viscous fluid, friction, and spring damping force. As an example, dual quaternions are used here to derive the Lagrange dynamic equations of a robot manipulator.