Next Article in Journal
Higher-Order Iteration Schemes for Solving Nonlinear Systems of Equations
Previous Article in Journal
Identification of Source Term for the Time-Fractional Diffusion-Wave Equation by Fractional Tikhonov Method
Previous Article in Special Issue
Some New Applications of Weakly ℋ-Embedded Subgroups of Finite Groups
Open AccessArticle

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

Department of Information Engineering, Marches Polytechnic University, Brecce Bianche Rd., I-60131 Ancona, Italy
Mathematics 2019, 7(10), 935; https://doi.org/10.3390/math7100935
Received: 3 September 2019 / Revised: 27 September 2019 / Accepted: 7 October 2019 / Published: 10 October 2019
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. View Full-Text
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 Lagrange–d’Alembert principle; non-conservative dynamical system; Euler–Poincaré equations; gyrostat satellite; quadcopter drone; forward Euler method; explicit Runge–Kutta method; Lie group
Show Figures

Figure 1

MDPI and ACS Style

Fiori, S. Model Formulation Over Lie Groups and Numerical Methods to Simulate the Motion of Gyrostats and Quadrotors. Mathematics 2019, 7, 935.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop