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Mechanics of particles for fluid dynamics: derivation of dissipative equations of motion using the principle of least action and fractional derivatives

D. Nerukh

Aston University


https://vkvideo.ru/video-222947497_456239116
https://youtu.be/IGGyojwM4iA

Аннотация: Equations of motion for systems with forces proportional to velocity are derived from the principle of least action using classical Euler-Lagrange equation and Lagrangian that contains terms responsible for energy dissipation. These terms are expressed through fractional derivatives of the coordinate of order $0 < \alpha < 1$.
This approach naturally leads to the introduction of non-uniform flow of time in dissipative processes. It incorporates inhomogeneous velocity without unphysical approximations. The fractional term in the Lagrangian provides correct Euler-Lagrange and, ultimately, Hamilton equations with energy dissipation rate defined by $\alpha$.
Smooth, gradual transition from classical mechanics (for example, Molecular Dynamics of point masses) to fluid dynamics (Navier-Stokes) can be realised using this approach.

Язык доклада: английский


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