Helmholtz theorem (classical mechanics)

The Helmholtz theorem of classical mechanics reads as follows: Let be the Hamiltonian of a one-dimensional system, where is the kinetic energy and is a "U-shaped" potential energy profile which depends on a parameter .Let denote the time average. Let Then

Helmholtz theorem (classical mechanics)

The Helmholtz theorem of classical mechanics reads as follows: Let be the Hamiltonian of a one-dimensional system, where is the kinetic energy and is a "U-shaped" potential energy profile which depends on a parameter .Let denote the time average. Let Then