Consider the functional S[y] = − y(2)² + √² ² + [² dx (31/1²) 2 with right-hand boundary condition y(3) = 2, subject to the constraint Cl[y] = ₁ dx 2 6 y x² = -1. (i) Give the auxiliary functional S[y] in terms of a Lagrange multiplier X. (ii) Consider an admissible variation y + ch of a path y. By using the boundary condition and by integrating by parts, obtain the Gâteaux differential AS[y, h]. (iii) Find the Euler-Lagrange equation and the boundary condition at x = 2 for a stationary path y.
Consider the functional S[y] = − y(2)² + √² ² + [² dx (31/1²) 2 with right-hand boundary condition y(3) = 2, subject to the constraint Cl[y] = ₁ dx 2 6 y x² = -1. (i) Give the auxiliary functional S[y] in terms of a Lagrange multiplier X. (ii) Consider an admissible variation y + ch of a path y. By using the boundary condition and by integrating by parts, obtain the Gâteaux differential AS[y, h]. (iii) Find the Euler-Lagrange equation and the boundary condition at x = 2 for a stationary path y.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
H4.
![(a) Consider the functional
S[y] =-y(2)² +
+ L² dx (31²)
with right-hand boundary condition y(3) = 2, subject to the
constraint
CM = [₁²₁
Cly
dx
6 y
= -1.
(i)
Give the auxiliary functional S[y] in terms of a Lagrange
multiplier X.
(ii) Consider an admissible variation y + ch of a path y. By using
the boundary condition and by integrating by parts, obtain
the Gâteaux differential AS[y, h].
(iii) Find the Euler-Lagrange equation and the boundary
condition at x = 2 for a stationary path y.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee47b394-b23a-435b-9dba-cf0154d9df92%2Fdc9194e4-8513-4ad6-bb02-bd4bfaa09d9c%2F0j71z6_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Consider the functional
S[y] =-y(2)² +
+ L² dx (31²)
with right-hand boundary condition y(3) = 2, subject to the
constraint
CM = [₁²₁
Cly
dx
6 y
= -1.
(i)
Give the auxiliary functional S[y] in terms of a Lagrange
multiplier X.
(ii) Consider an admissible variation y + ch of a path y. By using
the boundary condition and by integrating by parts, obtain
the Gâteaux differential AS[y, h].
(iii) Find the Euler-Lagrange equation and the boundary
condition at x = 2 for a stationary path y.
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