Field momentum and gyroscopic dynamics of classical systems with topological defects

Abstract

The standard relation between the field momentum and the force is generalized for the system with a field singularity: in addition to the regular force, there appear the singular one. This approach is applied to the description of the gyroscopic dynamics of the classical field with topological defects. The collective variable Lagrangian description is considered for gyroscopical systems with account of singularities. Using this method we describe the dynamics of two-dimensional magnetic solitons. We establish a relation between the gyroscopic force and the singular one. An effective Lagrangian description is discussed for the magnetic soliton dynamics.