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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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Basic Dynamics of Point Particles and Collections

Basic Dynamics of Point Particles and Collections

(p.3) 1 Basic Dynamics of Point Particles and Collections
Analytical Mechanics for Relativity and Quantum Mechanics

Oliver Johns

Oxford University Press

Modern mechanics begins with the publication in 1687 of Isaac Newton’s Principia, in which he explains mathematically the motions of planets, moons, comets, and tides in what is now known as the three laws of motion. This chapter assumes that Newton’s three laws of motion refer fundamentally to point particles. After deriving the laws of momentum, angular momentum, and work-energy for point particles, it is shown that, given certain plausible and universally accepted additional axioms, essentially the same laws can be proved to apply to macroscopic bodies, considered as collections of the elementary point particles. This chapter also discusses Newton’s space and time, single point particle, collective variables, the law of momentum for collections, the law of angular momentum for collections, the work-energy theorem for collections, potential and total energy for collections, the center of mass, center of mass and momentum, center of mass and angular momentum, center of mass and torque, change of angular momentum, center of mass and the work-energy theorems, center of mass as a point particle, and special results for rigid bodies.

Keywords:   Isaac Newton, point particles, collections, laws of motion, angular momentum, macroscopic bodies, work-energy theorem, center of mass, rigid bodies

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