Field momentum and gyroscopic dynamics of classical systems with topological defects

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 appears 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 taking into account 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.