Rigid Body Dynamics using Equimomental Systems of Point-Masses

Journal article

Laus, L. and Selig, J. (2019). Rigid Body Dynamics using Equimomental Systems of Point-Masses. Acta Mechanica. pp. 1-16. https://doi.org/10.1007/s00707-019-02543-3
AuthorsLaus, L. and Selig, J.
Abstract

The inertia matrix of any rigid body is the same as the inertia matrix of some system of four point-masses. In this work the possible disposition of these point-masses is investigated. It is found that every system of possible point-masses with the same inertia matrix can be parameterised by the elements of the orthogonal group in four dimensions modulo permutation of the points. It is shown that given a fixed inertia matrix, it is possible to find a system of point-masses with the same inertia matrix but where one of the points is located at some arbitrary point. It is also possible to place two point-masses on an arbitrary line or three of the points on an arbitrary plane. The possibility of placing some of the point- masses at infinity is also investigated. Applications of these ideas to rigid-body dynamics is considered. The equation of motion for a rigid body is derived in terms of a system of four point-masses. These turn out to be very simple when written in a 6-vector notation.

Year2019
JournalActa Mechanica
Journal citationpp. 1-16
PublisherSpringer
ISSN1619-6937
Digital Object Identifier (DOI)https://doi.org/10.1007/s00707-019-02543-3
Publication dates
Print14 Oct 2019
Publication process dates
Accepted07 Sep 2019
Deposited10 Sep 2019
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Open
Accepted author manuscript
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