The Hannay angle is defined in the context of action-angle coordinates. In an initially time-invariant system, an action variable I α α is a constant. After introducing a periodic perturbation λ λ ( t ) , the action variable I α α becomes an adiabatic invariant, and the Hannay angle θ θ α α H for its corresponding angle variable can be calculated according to the path integral that represents an evolution in which the perturbation λ λ ( t ) gets back to the original value θ θ α α H = − − ∂ ∂ ∂ ∂ I α α ∮ ∮ p ⋅ ⋅ ∂ ∂ q ∂ ∂ λ λ d λ λ = − − ∂ ∂ I α α ∬ ∬ ω ω where p and q are canonical variables of the Hamiltonian, and ω ω is the symplectic Hamiltonian 2-form.