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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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

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

First available in Project Euclid: 18 December 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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