Let a < b, A and B be constants. Gâteaux differential of the functional ·b [* dx (y² +w²y² + 2yx¹), y(a)=A, y(b) = B, a S[y] = d. where w is a positive constant. Using the Gateaux differential show that the stationary path of S[y] satisfies the Euler-Lagrange equation,
Let a < b, A and B be constants. Gâteaux differential of the functional ·b [* dx (y² +w²y² + 2yx¹), y(a)=A, y(b) = B, a S[y] = d. where w is a positive constant. Using the Gateaux differential show that the stationary path of S[y] satisfies the Euler-Lagrange equation,
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let a < b, A and B be constants.
Gâteaux differential of the functional
S[y] = d
dx (y² +w²y² + 2yxª), y(a)= A,
y(a) =
d'y
dx²
where is a positive constant.
Using the Gateaux differential show that the stationary path of
S[y] satisfies the Euler-Lagrange equation,
A, _y(b) = B,
- w²y = x¹, y(a) = A, y(b) = B,
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59d44c96-efb1-4f3c-83b3-5a6a84cf94cb%2Fa2afef41-4567-4340-8f29-376a58f77247%2Fje8qfvs_processed.png&w=3840&q=75)
Transcribed Image Text:Let a < b, A and B be constants.
Gâteaux differential of the functional
S[y] = d
dx (y² +w²y² + 2yxª), y(a)= A,
y(a) =
d'y
dx²
where is a positive constant.
Using the Gateaux differential show that the stationary path of
S[y] satisfies the Euler-Lagrange equation,
A, _y(b) = B,
- w²y = x¹, y(a) = A, y(b) = B,
-
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