Non-Lagrangian equations of motion and the momentum non-conservation

TL;DR

This paper explores a geometrical model where the affine connection relates to the electromagnetic field, demonstrating the possibility of momentum non-conservation and illustrating it with a toy device in a magnetic field.

Contribution

It introduces a novel geometrical framework linking affine connection to electromagnetic fields, showing how momentum non-conservation can occur within this model.

Findings

Momentum non-conservation is possible in the proposed geometrical model.

A toy device demonstrates the effect of momentum non-conservation in a magnetic field.

The model provides a new perspective on electromagnetic interactions and motion.

Abstract

In the framework of a geometrical model, in which the affine connection of a space is expressed in terms of the electromagnetic field, a possibility of the momentum non-conservation is shown. A toy device with an object moving in a magnetic field is presented for an illustration of the effect.