Communications in Mathematical Analysis

On Hamiltonian Theory for Rotating Charge Coupled to the Maxwell Field

G. Burlak, V. Imaykin, and A. Merzon

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Abstract

It is known that the Maxwell-Lorentz equations with Abraham’s rotating extended electron can be derived from the the Hamilton least action principle applying the variational Poincaré equations on the Lie group SO(3). We prove that, rewritten in the Euler angles, these equations imply the standard Euler-Lagrange and Hamiltonian equations.

Article information

Source
Commun. Math. Anal., Volume 17, Number 2 (2014), 24-33.

Dates
First available in Project Euclid: 18 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.cma/1418919753

Mathematical Reviews number (MathSciNet)
MR3292957

Zentralblatt MATH identifier
1297.15037

Subjects
Primary: 35Q61: Maxwell equations 35Q70: PDEs in connection with mechanics of particles and systems

Keywords
Maxwell-Lorentz equations Hamilton least action principle Poincaré equations on the Lie group SO(3) Euler angles Abraham’s rotating extended electron Euler- Lagrange equations Hamiltonian equations

Citation

Burlak, G.; Imaykin, V.; Merzon, A. On Hamiltonian Theory for Rotating Charge Coupled to the Maxwell Field. Commun. Math. Anal. 17 (2014), no. 2, 24--33. https://projecteuclid.org/euclid.cma/1418919753


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