I have an assessment/investigation coming up in my math class for which I plan to derive the equations of motion for the slingshot maneuver/gravity assist using Lagrangian mechanics. So far, I am familiar with the process of deriving kinematic equations for projectile motion systems using the Lagrangian formalism. My initial hunch is to compute the Lagrangian using the expressions for kinetic and potential energies and use the Euler-Lagrange equation to derive the equations.
How feasible do you guys think this topic is and what is your general opinion about it? I'm a high school senior.