Derivation of atmospheric flight equations of motion using lagrangian dynamics and its application to aerocapture

In this work, the widely utilized atmospheric flight equations of motion are derived utilizing Lagrangian dynamics. Lagrange’s equations are utilized to ascertain the equations of motion for atmospheric flight in an spherical rotating planet. The resulting equations are shown to agree with their Newtonian-derived counterparts found in literature. The exercise of utilizing Lagrangian dynamics is shown to provide an elegant approach to obtaining the equations of motion and is shown to be easily expandable to incorporate additional terms including planetary oblateness and aerodynamic side-force. Transformation between planet-relative and inertial state vector coordinates are presented along with relations to Keplerian orbital elements. The derived equations of motion are utilized in the formulation of the aerocapture flight path angle theoretical corridor width. Numerical simulations for a Mars aerocapture scenario are presented to demonstrate the numerical integration results of the derived equations of motion.