Question

Derive the Euler-Lagrange equations and the associated boundary conditions the functional (Reference homework solution to give details of the processing) 2

Answer 1

Solution:

given that

  Derive the Euler-Lagrange equations and the associated boundary conditions the functional (Reference homework solution.
"Implies The functional is (n (y)) = integrals^L_0 (s y""^2 + q y^2) dx/integrals^L_0 (r y'^2 (x) middot dx for the given t elementof R, and a function a z define f (t) = pi (y + t 2) = integrals^2_0 [s (y + t 2)""^2 (lambda) + epsilon (y + t 2)^2 (x)] dx/integrals^L_0 r (y + t z)^12 dx. Implies Let or denote the numerator and the denominator as g (t), h (t) respectively. Implies TO compute the Euler-Lagrange equation use consider t = 0 is the critical point of f when y is a critical point of n f' (0) = g' (0)/h (0) = g (0) h' (0)/h^2 (0). Implies g' (0) = d/dt integrals^L_0 [s (y + t 2)""^2 (x) + epsilon (y + t 2)^2 (x)] dx]_t = 0 implies 2 integrals^L_0 s (y + t 2)"" 2"" + epsilon (y + t 2) z dx