Model Formulation Over Lie Groups and Numerical Methods to Simulate the Motion of Gyrostats and Quadrotors

Abstract

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.

Keywords

• lagrange–d’alembert principle
• non-conservative dynamical system
• euler–poincaré equations
• gyrostat satellite
• quadcopter drone
• forward euler method
• explicit runge–kutta method
• lie group