An Analytical Mechanics Framework for Flow-Oscillator Modeling of Vortex-Induced Bluff-Body Oscillations by Sohrob Mottaghi & Rene Gabbai & Haym Benaroya

Author:Sohrob Mottaghi & Rene Gabbai & Haym Benaroya
Language: eng
Format: epub
ISBN: 9783030261337
Publisher: Springer International Publishing

5.1.7 The Euler–Lagrange Equations and the Natural Boundary Conditions

Collecting like terms in Eq. 5.25 gives

Arguing in the usual way that the variations are arbitrary in leads to the Euler–Lagrange (EL) equation

(5.26)

A similar argument regarding the variations on and leads to the natural boundary conditions

(5.27)

(5.28)

Substituting Eq. 5.11 into Eq. 5.26 yields the components of the balance of linear momentum equation for a Newtonian viscous compressible fluid with constant viscosity coefficients:

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