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

Author

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  • Simone Fiori

    (Department of Information Engineering, Marches Polytechnic University, Brecce Bianche Rd., I-60131 Ancona, Italy)

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.

Suggested Citation

  • Simone Fiori, 2019. "Model Formulation Over Lie Groups and Numerical Methods to Simulate the Motion of Gyrostats and Quadrotors," Mathematics, MDPI, vol. 7(10), pages 1-35, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:935-:d:274932
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    References listed on IDEAS

    as
    1. Vladimir Aslanov, 2015. "Behavior of a Free Dual-Spin Gyrostat with Different Ratios of Inertia Moments," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-10, February.
    2. Zoran Benic & Petar Piljek & Denis Kotarski, 2016. "Mathematical modelling of unmanned aerial vehicles with four rotors," Interdisciplinary Description of Complex Systems - scientific journal, Croatian Interdisciplinary Society Provider Homepage: http://indecs.eu, vol. 14(1), pages 88-100.
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    Cited by:

    1. Simone Fiori & Luca Bigelli & Federico Polenta, 2022. "Lie-Group Type Quadcopter Control Design by Dynamics Replacement and the Virtual Attractive-Repulsive Potentials Theory," Mathematics, MDPI, vol. 10(7), pages 1-37, March.

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