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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. It was first introduced by him in 1873. [ 1 ]
The central quantity of Lagrangian mechanics is the Lagrangian, a function which summarizes the dynamics of the entire system. Overall, the Lagrangian has units of energy, but no single expression for all physical systems. Any function which generates the correct equations of motion, in agreement with physical laws, can be taken as a Lagrangian.
In probability theory and statistics, the Rayleigh distribution is a continuous probability distribution for nonnegative-valued random variables. Up to rescaling, it coincides with the chi distribution with two degrees of freedom .
Rayleigh (1873) [38] (and in Sections 81 and 345 of Rayleigh (1896/1926) [28]) introduced the dissipation function for the description of dissipative processes involving viscosity. More general versions of this function have been used by many subsequent investigators of the nature of dissipative processes and dynamical structures.
Dissipation function may refer to Rayleigh's dissipation function; Dissipation function under the fluctuation theorem This page was last edited on 28 ...
With respect to the extended Euler-Lagrange formulation (See Lagrangian mechanics § Extensions to include non-conservative forces), the Rayleigh dissipation function represents energy dissipation by nature. Therefore, energy is not conserved when . This is similar to the velocity dependent potential.
Pages in category "Functions and mappings" ... Range of a function; Rayleigh dissipation function; Reflection (mathematics) Richardson's theorem; Ridge function;
Rayleigh dissipation function; Rheonomous; S. Scleronomous; T. Tautological one-form; Total derivative; V. Virtual displacement This page was last edited on 22 ...