We show that the action of a dynamical system can be supplemented by an effective action for its environment to reproduce arbitrary coordinate dependent ohmic dissipation and gyroscopic forces. The action is a generalization of the harmonic bath model and describes a set of massless interacting scalar fields in an auxiliary space coupled to the original system at the boundary. A certain limit of the model implements nonholonomic constraints. In the case of dynamics with nonlinearly realized symmetries the effective action takes the form of a two-dimensional nonlinear $\sigma$ model. It provides a basis for application of path integral methods to general dissipative and nonholonomic systems.

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• Dissipative dynamics
• Effective field theory
• Nonlinear sigma model
• Path integrals
• Spontaneous symmetry breaking
• Continuous symmetries
• Dissipative particle dynamics
• Path-integral methods