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
Authors | Laus, L. and Selig, J. |
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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. |
Year | 2019 |
Journal | Acta Mechanica |
Journal citation | pp. 1-16 |
Publisher | Springer |
ISSN | 1619-6937 |
Digital Object Identifier (DOI) | https://doi.org/10.1007/s00707-019-02543-3 |
Publication dates | |
14 Oct 2019 | |
Publication process dates | |
Accepted | 07 Sep 2019 |
Deposited | 10 Sep 2019 |
Publisher's version | License File Access Level Open |
Accepted author manuscript | License File Access Level Controlled |
https://openresearch.lsbu.ac.uk/item/87zy2
Download files
Publisher's version
Laus-Selig2019_Article_RigidBodyDynamicsUsingEquimome.pdf | ||
License: CC BY 4.0 | ||
File access level: Open |
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