Orbital Acceleration Using Product of Exponentials

TL;DR

This paper extends the Product of Exponentials formulation to orbital mechanics by deriving the second derivative, providing a more complete description of satellite motion with all six orbital elements considered.

Contribution

It introduces the second derivative of the PoE formula for orbital mechanics, enabling a comprehensive analysis of orbital acceleration in a two-body system.

Findings

Derived the second derivative of the PoE formula for orbital motion

Enhanced the description of satellite dynamics with all orbital elements

Broadens applications in orbital analysis and control

Abstract

The Product of Exponentials (PoE) formulation is most commonly used in the field of robotics, but has recently been adapted for use in describing orbital motion. The PoE formula for orbital mechanics is an alternate method for defining and drawing an orbit based on its orbital elements set. Currently the PoE formula for orbital mechanics has only been derived through the first derivative (velocity). This work explores the second derivative of the adapted PoE formula for orbital mechanics, which gives a more complete description of the orbital motion of a satellite in a two-body system. This comprehensive approach employs a unified approach to account for all six time-varying orbital elements, therefore broadening the scope of the research and applications.