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The elliptope and bounds in the rotational dynamics of rigid bodies

Área de Matemática Aplicada, Departamento de Ingeniería y Tecnología de Computadores (DITEC), Facultad de Informática, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spain

E-mail Address: sferrer@um.es

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Francisco J. Molero

Área de Matemática Aplicada, Departamento de Ingeniería y Tecnología de Computadores (DITEC), Facultad de Informática, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spain

E-mail Address: javier.moleromadrid@gmail.com

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, and

Francisco Crespo

https://orcid.org/0000-0002-5930-8523

Sistemas Dinámicos y Aplicaciones GISDA, Departamento de Matemática, Facultad de Ciencias, Universidad del Bío-Bío, Avenida Collao 1202, Casilla 5-C, Concepción, Región del Bío-Bío, Chile

E-mail Address: fcrespo@ubiobio.cl

Corresponding author.

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https://doi.org/10.1142/S2972458924500084Cited by:0 (Source: Crossref)

Abstract

The main result of this paper establishes a new polynomial relation among several projections of the angular momentum vector on the spatial and moving frames involved in the rotational dynamics of rigid bodies. This relation is surprisingly simple to derive and provides a geometric insight into the attitude dynamics of bodies with axial symmetry, explaining the bounds for the nutation angle $θ$ $𝜃$ .

Keywords:

AMSC: 70E15, 70E40, 70E99

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