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Analytical Mechanics for Relativity and Quantum Mechanics$
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Oliver Johns

Print publication date: 2005

Print ISBN-13: 9780198567264

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198567264.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2022. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use.date: 27 January 2022

Kinematics of Rotation

Kinematics of Rotation

Chapter:
(p.152) 8 Kinematics of Rotation
Source:
Analytical Mechanics for Relativity and Quantum Mechanics
Author(s):

Oliver Johns

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198567264.003.0008

This chapter deals with techniques needed to define the location and orientation of a moving rigid body. Rigid bodies are characterised and the center of mass of a rigid body is discussed along with rotation operators, rotation matrices, some properties of rotation operators, proper and improper rotation operators, rotation group, kinematics of a rigid body, differentiation of a rotation operator, angular velocity vector, velocities of the masses of a rigid body, Savio’s theorem, infinitesimal rotation, addition of angular velocities, fundamental generators of rotations, rotation with a fixed axis, expansion of fixed-axis rotation, eigenvectors of the fixed-axis rotation operator, Euler theorem, rotation of operators, rotation of the fundamental generators, rotation of a fixed-axis rotation, parameterisation of rotation operators, differentiation of parameterised operator, Euler angles, fixed-axis rotation from Euler angles, time derivative of a product, angular velocity from Euler angles, active and passive rotations, passive transformation of vector components, passive transformation of matrix elements, body derivative, passive rotations and rigid bodies, and passive use of Euler angles.

Keywords:   rigid bodies, rotation operators, kinematics, angular velocity vector, Savio’s theorem, Euler theorem, fixed-axis rotation, eigenvectors, body derivative

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