  We formulate the theory of shortcuts to adiabaticity in classical mechanics.
For a reference Hamiltonian, the counterdiabatic term is constructed from the
dispersionless Korteweg-de Vries (KdV) hierarchy. Then the adiabatic theorem
holds exactly for an arbitrary choice of time-dependent parameters. We use the
Hamilton-Jacobi theory to define the generalized action. The action is
independent of the history of the parameters and is directly related to the
adiabatic invariant. The dispersionless KdV hierarchy is obtained from the
classical limit of the KdV hierarchy for the quantum shortcuts to adiabaticity.
This correspondence suggests some relation between the quantum and classical
adiabatic theorems.
