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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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Relativistic Mechanics

Relativistic Mechanics

(p.376) 16 Relativistic Mechanics
Analytical Mechanics for Relativity and Quantum Mechanics

Oliver Johns

Oxford University Press

It was apparent from its beginning that special relativity developed as the invariance theory of electrodynamics would require a modification of Newton’s three laws of motion. This chapter discusses that modified theory. The relativistically modified mechanics is presented and then recast into a fourvector form that demonstrates its consistency with special relativity. Traditional Lagrangian and Hamiltonian mechanics can incorporate these modifications. This chapter also discusses the momentum fourvector, fourvector form of Newton’s second law, conservation of fourvector momentum, particles of zero mass, traditional Lagrangian and traditional Hamiltonian, invariant Lagrangian, manifestly covariant Lagrange equations, momentum fourvectors and canonical momenta, extended and invariant Hamiltonian, manifestly covariant Hamilton equations, the Klein-Gordon equation, the Dirac equation, the manifestly covariant N-body problem, covariant Serret-Frenet theory, Fermi-Walker transport, and example of Fermi-Walker transport.

Keywords:   relativistic mechanics, special relativity, laws of motion, Hamiltonian mechanics, Lagrange equations, Dirac equation, momentum fourvectors, Klein-Gordon equation, Serret-Frenet theory, Fermi-Walker transport

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