Feynman-Dyson proof of the Feshbach-Tikochinsky equations of motion

We extend the approach of the Feynman-Dyson proof of the Lorentz force law to dissipative systems. The Feshbach-Tikochinsky equations for a damped har monic oscillator are derived by considering localizable Poisson brackets fo r dissipative systems on an extension of the velocity phase space by double d phase space variables whose initial values are related to quantum effects . The form of the Lagrangian is also determined. The solution involves a di scussion of the inverse problem of the calculus of variations.