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On the line geometry of rigid-body inertia.

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Title: On the line geometry of rigid-body inertia.
Authors: Selig, J.1 seligjm@lsbu.ac.uk, Martins, D.2 daniel@emc.ufsc.br
Source: Acta Mechanica. Nov2014, Vol. 225 Issue 11, p3073-3101. 29p.
Subjects: Rigid bodies, Line geometry, Displacement (Mechanics), Least squares, Problem solving
Abstract: In this work, several classical ideas concerning the geometry of the inertia of a rigid body are revisited. This is done using a modern approach to screw theory. A screw, or more precisely a twist, is viewed as an element of the Lie algebra to the group of proper rigid-body displacements. Various moments of inertia, about lines, planes and points are considered as geometrical objects resulting from least-squares problems. This allows relations between the various inertias to be found quite simply. A brief review of classical line geometry is given; this includes an outline of the theory of the linear line complex and a brief introduction to quadratic line complexes. These are related to the geometry of the inertia of an arbitrary rigid body. Several classical problems concerning the mechanics of rigid bodies subject to impulsive wrenches are reviewed. We are able to correct a small error in Ball's seminal treatise. The notion of spatial percussion axes is introduced, and these are used to solve a problem concerning the diagonalisation of the mass matrix of a two-joint robot. [ABSTRACT FROM AUTHOR]
Copyright of Acta Mechanica is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: In this work, several classical ideas concerning the geometry of the inertia of a rigid body are revisited. This is done using a modern approach to screw theory. A screw, or more precisely a twist, is viewed as an element of the Lie algebra to the group of proper rigid-body displacements. Various moments of inertia, about lines, planes and points are considered as geometrical objects resulting from least-squares problems. This allows relations between the various inertias to be found quite simply. A brief review of classical line geometry is given; this includes an outline of the theory of the linear line complex and a brief introduction to quadratic line complexes. These are related to the geometry of the inertia of an arbitrary rigid body. Several classical problems concerning the mechanics of rigid bodies subject to impulsive wrenches are reviewed. We are able to correct a small error in Ball's seminal treatise. The notion of spatial percussion axes is introduced, and these are used to solve a problem concerning the diagonalisation of the mass matrix of a two-joint robot. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Acta Mechanica is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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