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

Simone Fiori
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Simone Fiori: Department of Information Engineering, Marches Polytechnic University, Brecce Bianche Rd., I-60131 Ancona, Italy

Mathematics, 2019, vol. 7, issue 10, 1-35

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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