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Title of Journal: Nonlinear Dyn

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Abbravation: Nonlinear Dynamics

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Springer Netherlands

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DOI

10.1007/s13143-011-1007-6

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1573-269X

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Minimum distance and optimal transformations on SO

Authors: Andrew J Sinclair John E Hurtado John L Junkins
Publish Date: 2007/12/21
Volume: 54, Issue: 3, Pages: 181-187
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Abstract

The group of special or proper orthogonal matrices SON is used throughout engineering mechanics in the analysis and representation of mechanical systems In this paper a solution is presented for the optimal transformation between two elements of SON The transformation is assumed to occur during a specified finite time and a cost function that penalizes the transformation rates is utilized The optimal transformation is found as a constantrate rotation in each of the principal planes relating the two elements Although the kinematics of SON are nonlinear and governed by Poisson’s equation the solution is found to be a linear function of the generalized principal angles This is made possible by the extension of principalrotation kinematics from threedimensional rotations to the general SON group This extension relates the Ndimensional angular velocity to the derivatives of the principal angles The cost of the optimal transformation the square root of the sum of the principal angles squared also provides a useful measure for the angular distance between two elements of SON

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