I would invite you to immediately look at my attached pdf and LaTeX file for my introduction and appetizer on “Symmetries of Rocket Dynamics”:
I recap the Euler-Poincarè reduction for the Lagrangian of a free (and non-free) rigid body and discuss the constraints and time steps for the Time Optimal Attitude Control Problem for a Rigid Body. Finally, what I’d like to motivate is an implementation of the Discrete-Time Time Optimal Attitude Control algorithm in.
It concerns me greatly that the Falcon 9R tipped over and dropped and exploded. This had been a second attempt at a first stage rocket landing.
It would be interesting to explore if all aspects of mathematical physics was employed and implemented into the dynamic stability and control of Falcon 9R. In particular, it would be interesting to look at what the symmetry of the Lie group SO(3), the group of rotations, says about the dynamics (i.e. equations of motion) of the rocket as a rigid-body.