Rayleigh Dissipation Function

In physics, the Rayleigh dissipation function, named after 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 $\vec$ can be written as $\vec_f = -\vec\cdot\vec$, the Rayleigh dissipation function can be defined for a system of $N$ particles as
:$G(v) = \frac \sum_^N ( k_x v_^2 + k_y v_^2 + k_z v_^2 ).$

The force of friction is negative the velocity gradient of the dissipation function, $\vec_f = -\nabla_v G(v)$. 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 ''Q_j'' term of Lagrange's equations.

References

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Functions and mappings
Lagrangian mechanics

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