Euler-Lagrange equation


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Euler-Lagrange equation

[¦ȯi·lər lə′grānj i‚kwā·zhən]
(mathematics)
A partial differential equation arising in the calculus of variations, which provides a necessary condition that y (x) minimize the integral over some finite interval of f (x,y,y ′) dx, where y ′ = dy/dx; the equation is (δƒ(x,y,y ′)/δ y) - (d/dx)(δƒ(x,y,y ′)/δ y ′) =0. Also known as Euler's equation.
References in periodicals archive ?
We consider the Euler-Lagrange equation using the identity of Proposition 4.
Emmy Noether's theorem Noether, (1918) is a profound reinterpretation of the Euler-Lagrange equation.
The Euler-Lagrange equation d/dt([partial derivative]L/ [partial derivative][?
The associated Euler-Lagrange equation for the unknown [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Adding null Lagrangian to any integrand does not affect the variational Euler-Lagrange equation, [2].
As stated above, the Euler-Lagrange equation (3) is the system's equation of motion.
In the work ,,Oscillation matrixes, oscillation cores and low oscillations of mechanical systems" Gantmacher and Krein [12] showed that Stieltjes continued fractions are solutions of the Euler-Lagrange equation for low amplitude oscillations of chain systems.
The principle of stationary action [delta]S = 0 respectively induced the Euler-Lagrange equations
The Euler-Lagrange equations of motion for an n-link master and slave robot are given as (Chopra, et al.
Making use of the free energy function (2) and Euler-Lagrange equations, we obtain the equations of motion