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Motion of a classical particle with spin

Published online by Cambridge University Press:  24 October 2008

J. R. Ellis
J. R. Ellis
Affiliation:
University of Sussex, Brighton
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Abstract

The helical solutions of the Frenkel-Thomas equations for a free spinning particle are discussed following manifestly covariant lines. For the purposes of expressing the equations in Lagrangian and Hamiltonian form, the definition of spin by H. C. Corben is not entirely satisfactory being frame-dependent. The use of a spin ‘four-vector’ is discussed which makes the solution of the equations shorter and more elegant than that of Corben. Such a derivation necessitates the use of the Frenet-Serret formulae. By basing a Lagrangian formalism on this definition of spin we show that the covariant Euler-Lagrange equations (with multipliers) lead directly to the Frenkel-Thomas equations. Such a derivation is thus an improvement on those of other authors and suggests a more suitable canonical formalism for these equations.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 78 , Issue 1 , July 1975 , pp. 145 - 156
Copyright
Copyright © Cambridge Philosophical Society 1975

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