Rayleigh Dissipation Function

The Rayleigh dissipation function, named after Lord Rayleigh, who introduced it in 1873, is a function used in Lagrangian mechanics to account for the effect of velocity-proportional frictional forces that ordinary Lagrangian mechanics, built from kinetic and potential energy alone, cannot represent directly. When the frictional force on a particle is proportional to its velocity, the function can be written as half the sum, over every particle in the system, of frictional damping coefficients multiplied by the squares of the particle's velocity components; the frictional force is then the negative gradient of this function with respect to velocity, entering the Euler-Lagrange equations as a non-conservative term. Since the 1970s the function is more often called the Rayleigh dissipation potential, and the original quadratic form has since been generalized to convex, non-quadratic dissipation potentials that produce nonlinear friction laws such as Coulomb friction and plasticity. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/