Answered: Consider the following inertia tensor.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider the following inertia tensor. Calculate a rotation of the coordinate system by an angle θ about the z axis. Evaluate the transformed tensor elements and calculate rotation angle θ for which inertia tensor has only
diagonal elements. 0 ≤ ? ≤ pi.

1
(A + B) (A – B) 0
2
2
1
I =
1
5 (A – B) (A+ B) 0
2
|
2
C

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

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