Nonsingular Euler Parameterizations for Motion of a Point Mass in Atmospheric Flight

TL;DR

This paper introduces three nonsingular Euler parameterizations for modeling the translational motion of a point mass in atmospheric flight, avoiding singularities and trigonometric functions present in traditional methods, thus offering computational advantages.

Contribution

The paper develops novel Euler parameterizations that eliminate singularities and trigonometric functions in atmospheric flight modeling, improving computational efficiency over traditional methods.

Findings

The new parameterizations are nonsingular during vertical flight.

They demonstrate computational advantages over Euler angle-based methods.

An example confirms the effectiveness of the formulations.

Abstract

Three parameterizations are developed for modeling translational motion of a point mass in atmosphere flight over a central rotating body. Unlike well-known parameterizations such as spherical coordinate parameterizations, where position and velocity are parameterized using a magnitude an an Euler angle rotation sequence, the method presented in this research employs Euler parameters. Consequently, singularities and trigonometric functions are eliminated from the differential equations of motion. As a result, the new parameterizations presented in this paper offer computational advantages over standard parameterizations that employ Euler angle sequences. Finally, an example is studied where an atmospheric vehicle moves while in vertical flight, demonstrating the nonsingular nature of the formulations developed in this paper.