Explain what geometric problem. As there local or is solved fiese ond global constraint. d
Explain what geometric problem. As there local or is solved fiese ond global constraint. d
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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Question
![Date:
/20
Day
A
constrained extremisation Problem is expressed
as longronge-multiplier problem with objective
functional
I [x+x] = [[√√₂² ² + y² + 3 ² _k (t) (x² + y² +3²_R²³)]d²
where x = da etc. and integeral has appropriate
fixed limitat
with fixed values of X₂ Y and
Z at the endpoints.
a). Explain what geometric problem is solved here and
local or
global constraint.
for Variable x
As there
b)- show that ewler-longronge eq.
takes the form,
d
d
at
(7) = -ax
Also find Euler - Longronze ey's for y and 3
land write them in vector notation for vector
X = (x, y, z). Give Jemeterical interpretation chat
they tell you.
C). show that Beltrami-identity does not help you.
to solve the equation-
d). Let u be an arbitrary increasing fn of t. show
that
ƒ [√xx²)³+ (y^)³+ (3³) ³ ]du= [[] x² + y + 3³ ] du
where. x'=dx, Explain what this
du
signifies
geometrically and why this means that one can
assumes without loss of generality, that
11 = R along solution of the
Euler-long range equations -](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5fb4c48-e210-4c5e-a541-160a60a9de22%2F14fafc1d-5289-4394-b205-203967521b4a%2Fh03exit_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Date:
/20
Day
A
constrained extremisation Problem is expressed
as longronge-multiplier problem with objective
functional
I [x+x] = [[√√₂² ² + y² + 3 ² _k (t) (x² + y² +3²_R²³)]d²
where x = da etc. and integeral has appropriate
fixed limitat
with fixed values of X₂ Y and
Z at the endpoints.
a). Explain what geometric problem is solved here and
local or
global constraint.
for Variable x
As there
b)- show that ewler-longronge eq.
takes the form,
d
d
at
(7) = -ax
Also find Euler - Longronze ey's for y and 3
land write them in vector notation for vector
X = (x, y, z). Give Jemeterical interpretation chat
they tell you.
C). show that Beltrami-identity does not help you.
to solve the equation-
d). Let u be an arbitrary increasing fn of t. show
that
ƒ [√xx²)³+ (y^)³+ (3³) ³ ]du= [[] x² + y + 3³ ] du
where. x'=dx, Explain what this
du
signifies
geometrically and why this means that one can
assumes without loss of generality, that
11 = R along solution of the
Euler-long range equations -
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