528. A General Method for the Determination of Principal Axes and Moments of Inertia

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Paper

R D Manners: 528. A General Method for the Determination of Principal Axes and Moments of Inertia. 1966.

 

Abstract

Equations describing the principal axes and moments of inertia in two dimensions are developed from basic principles, introducing the concepts of direction cosines and the momental ellipsoid. An extension of these equations leads to the three dimensional case and a general solution of the eigenvalue problem suitable for hand computation. Details are provided on Mohr’s construction for the determination of inertias on any plane through the origin of the momental ellipsoid. The application of matrix tensor methods is illustrated by the development of the second order inertia tensor and Mohr’s two dimensional representation of inertia. The Appendix contains the completely detailed solution to a three dimensional inertia problem using methods developed in the paper.

 

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