Stability Conditions for Permanent Rotations of a Heavy Gyrostat with Two Constant Rotors

Víctor Lanchares, Manuel Iñarrea, Ana Isabel Pascual and Antonio Elipe
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Víctor Lanchares: Department of Mathematics and Computation, Universidad de La Rioja, 26006 Logroño, Spain
Manuel Iñarrea: Applied Physics, Universidad de La Rioja, 26006 Logroño, Spain
Ana Isabel Pascual: Department of Mathematics and Computation, Universidad de La Rioja, 26006 Logroño, Spain
Antonio Elipe: Department of Applied Mathematics, Universidad de Zaragoza, 50009 Zaragoza, Spain

Mathematics, 2022, vol. 10, issue 11, 1-17

Abstract: In this paper, we consider the motion of an asymmetric heavy gyrostat, when its center of mass lies along one of the principal axes of inertia. We determine the possible permanent rotations and, by means of the Energy-Casimir method, we give sufficient stability conditions. We prove that there exist permanent stable rotations when the gyrostat is oriented in any direction of the space, by the action of two spinning rotors, one of them aligned along the principal axis, where the center of mass lies. We also derive necessary stability conditions that, in some cases, are the same as the sufficient ones.

Keywords: gyrostat rotation; stability; Energy-Casimir method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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