ABSTRACT

The Lagrange planetary equations provide a convenient analytical description of how orbital elements evolve in the presence of dynamical perturbations. These equations, widely useful for characterizing or prescribing long term behavior of orbits in complex gravitational settings, are derived from a powerful mathematical tool referred to as Lagrange brackets. This seminar will cover the derivation behind these brackets before showcasing how they can be transitioned into their powerful Lagrange planetary equations form. This seminar is geared towards undergraduate students in their junior or senior year who have been exposed to basic orbital mechanics and differential equations.

BIOGRAPHY

John Martin is a NSF graduate research fellow and PhD candidate in the Aerospace Engineering Sciences department at the University of Colorado Boulder. He earned his Bachelor’s degree in Physics and Astronomy from the University of North Carolina at Chapel Hill and his Masters in Aerospace Engineering from CU Boulder. During his PhD, John worked with the Laboratory for Atmospheric and Space Physics as part of the attitude determination and control subsystem team for a Mars orbiter, and he is currently an active developer for the open-source high-fidelity astrodynamics simulation software Basilisk. His research focuses on the intersection between scientific machine learning and astrodynamics, exploring how tools like physics informed neural networks can be used to find novel solutions to complex differential equations. and characterizing their corresponding advantages over prior analytic methods.