Lie-Group Modeling and Numerical Simulation of a Helicopter

Helicopters are extraordinarily complex mechanisms. Such complexity makes it difficult to model, simulate and pilot a helicopter. The present paper proposes a mathematical model of a fantail helicopter type based on Lie-group theory. The present paper first recalls the Lagrange–d’Alembert–Pontryagin...

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Autores principales:	Alessandro Tarsi, Simone Fiori
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Lagrange–d’Alembert principle non-conservative dynamical system Euler–Poincaré equation helicopter model Lie group Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/5705e442d66b4cfe93650aced27fa693
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id	oai:doaj.org-article:5705e442d66b4cfe93650aced27fa693
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spelling	oai:doaj.org-article:5705e442d66b4cfe93650aced27fa6932021-11-11T18:14:59ZLie-Group Modeling and Numerical Simulation of a Helicopter10.3390/math92126822227-7390https://doaj.org/article/5705e442d66b4cfe93650aced27fa6932021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2682https://doaj.org/toc/2227-7390Helicopters are extraordinarily complex mechanisms. Such complexity makes it difficult to model, simulate and pilot a helicopter. The present paper proposes a mathematical model of a fantail helicopter type based on Lie-group theory. The present paper first recalls the Lagrange–d’Alembert–Pontryagin principle to describe the dynamics of a multi-part object, and subsequently applies such principle to describe the motion of a helicopter in space. A good part of the paper is devoted to the numerical simulation of the motion of a helicopter, which was obtained through a dedicated numerical method. Numerical simulation was based on a series of values for the many parameters involved in the mathematical model carefully inferred from the available technical literature.Alessandro TarsiSimone FioriMDPI AGarticleLagrange–d’Alembert principlenon-conservative dynamical systemEuler–Poincaré equationhelicopter modelLie groupMathematicsQA1-939ENMathematics, Vol 9, Iss 2682, p 2682 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Lagrange–d’Alembert principle non-conservative dynamical system Euler–Poincaré equation helicopter model Lie group Mathematics QA1-939
spellingShingle	Lagrange–d’Alembert principle non-conservative dynamical system Euler–Poincaré equation helicopter model Lie group Mathematics QA1-939 Alessandro Tarsi Simone Fiori Lie-Group Modeling and Numerical Simulation of a Helicopter
description	Helicopters are extraordinarily complex mechanisms. Such complexity makes it difficult to model, simulate and pilot a helicopter. The present paper proposes a mathematical model of a fantail helicopter type based on Lie-group theory. The present paper first recalls the Lagrange–d’Alembert–Pontryagin principle to describe the dynamics of a multi-part object, and subsequently applies such principle to describe the motion of a helicopter in space. A good part of the paper is devoted to the numerical simulation of the motion of a helicopter, which was obtained through a dedicated numerical method. Numerical simulation was based on a series of values for the many parameters involved in the mathematical model carefully inferred from the available technical literature.
format	article
author	Alessandro Tarsi Simone Fiori
author_facet	Alessandro Tarsi Simone Fiori
author_sort	Alessandro Tarsi
title	Lie-Group Modeling and Numerical Simulation of a Helicopter
title_short	Lie-Group Modeling and Numerical Simulation of a Helicopter
title_full	Lie-Group Modeling and Numerical Simulation of a Helicopter
title_fullStr	Lie-Group Modeling and Numerical Simulation of a Helicopter
title_full_unstemmed	Lie-Group Modeling and Numerical Simulation of a Helicopter
title_sort	lie-group modeling and numerical simulation of a helicopter
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/5705e442d66b4cfe93650aced27fa693
work_keys_str_mv	AT alessandrotarsi liegroupmodelingandnumericalsimulationofahelicopter AT simonefiori liegroupmodelingandnumericalsimulationofahelicopter
_version_	1718431886138671104

Lie-Group Modeling and Numerical Simulation of a Helicopter

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