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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, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 24 January 2022

Rotational Dynamics

Rotational Dynamics

(p.202) 9 Rotational Dynamics
Analytical Mechanics for Relativity and Quantum Mechanics

Oliver Johns

Oxford University Press

The successful description of the motion of a rigid body is one of the triumphs of Newtonian mechanics. Having learned in the previous chapter how to specify the position and orientation of a rigid body, this chapter deals with its natural motion under impressed external forces and torques. The dynamical theorems of collective motion are extended using rotation operators. Some basic facts about rigid-body motion are discussed, along with the inertia operator and the spin, inertia dyadic, kinetic energy of a rigid body, meaning of the inertia operator, principal axes, time evolution of the spin, torque-free motion of a symmetric body, Euler angles of the torque-free motion, body with one point fixed, time evolution with one point fixed, work-energy theorems, rotation with a fixed axis, symmetric top with one point fixed, initially clamped symmetric top, approximate treatment of the symmetric top, inertial forces, calculations of the Coriolis force, and the magnetic-Coriolis analogy.

Keywords:   rigid body, collective motion, torques, rotation operators, kinetic energy, work-energy theorems, Euler angles, Coriolis force, symmetric top

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