Model formulation over Lie groups and numerical methods to simulate the motion of gyrostats and quadrotors

The present paper recalls a formulation of non-conservative system dynamics through the Lagrange-d'Alembert principle expressed through a generalized Euler-Poincaré form of the system equation on a Lie group. The paper illustrates applications of the generalized Euler-Poincaré equations on the rotation groups to a gyrostat satellite and a quadcopter drone. The numerical solution of the dynamical equations on the rotation groups is tackled via a generalized forward Euler method and an explicit Runge-Kutta integration method tailored to Lie groups.