Abstract
An action principle is usually the starting point to describe physical systems, both particles and fields. A preliminary study usually considers fields as given, i.e. as external fields while particles are thought of as test particles, therefore only the point particle dynamics is dealt with. In this approach the Lagrangian function usually is the sum of three terms: a kinematic term which is quadratic in the velocities, a current-potential coupling term which is linear in the velocities, and a term which depends only on the positions, for instance the electrostatic potential.
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