This paper introduces two integrals which simplify calculation of the dynamic properties of magnetic domains. These integrals, over quadratic functions of the spatial derivatives of the magnetization, yield forces acting on a domain which correspond to the gyroscopic and dissipative terms in the Gilbert equation. The force integral corresponging to the gyroscopic term is found to be even less sensitive to the details of the spin distribution than the dissipative drag integral. Hard magnetic bubble domains are considered as an illustrative example.

• Received 27 November 1972

DOI:https://doi.org/10.1103/PhysRevLett.30.230