Oscillatory Movements and Dual Quaternions

Abstract.

This paper shows how dual quaternions can be a way to describe oscillatory movements. Dual quaternions are the algebraic counterpart of screws. This fact enables to get an alternative description of an harmonic oscillatory motion. In this way, we can arrive to model more complicated oscillatory movements for example, it is possible to get the solution of a classic PDE: the Wave Equation. Thus, following this idea we can describe the kinetic behavior (position, velocity and time) of an Oscillatory Movement by a dual-quaternion product.