Consider the functional S[y] = ay(1)² + [* dx ßy², y(0) = 0, with a natural boundary condition at x C{y] = Yy(1)² + [" dx w(x) y² = 1, where a, ẞ and y are nonzero constants. = 1 and subject to the constraint Show that the stationary paths of this system satisfy the Euler-Lagrange equation d²y β +\w(x) y = 0, y(0) = 0, (a− yλ) y(1) + ßy′(1) = 0, dx2 where is a Lagrange multiplier.
Consider the functional S[y] = ay(1)² + [* dx ßy², y(0) = 0, with a natural boundary condition at x C{y] = Yy(1)² + [" dx w(x) y² = 1, where a, ẞ and y are nonzero constants. = 1 and subject to the constraint Show that the stationary paths of this system satisfy the Euler-Lagrange equation d²y β +\w(x) y = 0, y(0) = 0, (a− yλ) y(1) + ßy′(1) = 0, dx2 where is a Lagrange multiplier.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.2: Partial Derivatives
Problem 25E
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