Nonsingular Parameterization for Modeling Translational Motion Using Euler Parameters

TL;DR

This paper introduces a novel singularity-free parameterization for modeling translational motion in 3D space using Euler parameters, offering mathematical and computational benefits over traditional methods.

Contribution

It presents a new parameterization method employing Euler parameters to avoid singularities and trigonometric complexities in translational motion modeling.

Findings

Reduces singularities in translational motion equations

Demonstrates computational efficiency over traditional methods

Provides clear mathematical advantages in examples

Abstract

A parameterization is described for quantifying translational motion of a point in three-dimensional Euclidean space. The parameterization is similar to well-known parameterizations such as spherical coordinates in that both position and velocity are decoupled into magnitude and orientation components. Unlike these standard parameterizations, where principal rotation sequences are employed, the method presented in this research employs Euler parameters. By using Euler parameters instead of Euler angles, singularities and trigonometric functions are removed from the equations of motion. The parameterization is demonstrated on two examples, where it is found that the new parameterization offers both mathematical and computational advantages over other commonly used parameterizations.