Rayleigh dissipation function

In physics, the Rayleigh dissipation function, named for Lord Rayleigh, is a function used to handle the effects of velocity-proportional frictional forces in Lagrangian mechanics. If the frictional force on a particle with velocity formula_1 can be written as formula_2, the Rayleigh dissipation function can be defined for a system of formula_3 particles as
The force of friction is negative the velocity gradient of the dissipation function, formula_5. The function is half the rate at which energy is being dissipated by the system through friction.
As friction is not conservative, it is included in the "Qj" term of Lagrange's equations.