show that Beltrami-identity does not help you. to solve the equation- + wint fo of t. show
show that Beltrami-identity does not help you. to solve the equation- + wint fo of t. show
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
![Day:
Date: //20
A constrained extremisation Problem is expressed
as longsonge-multiplier problem with objective
functional.
I [X³ X] = √ [√x² ² + y² + 3 2 _k (t) (x²+ y² +3²_R²) ]dt
where x = dxc etc. and intereral has appropriate
fixed limitat
with fixed values of Xoy and
7 at the endpoints.
a). Explain what geometric problem is solved fiere and
Is there a local or global constraint.
for Variable x
b)- show that ewler-longronge eq.
takes the form,
d
at
x
√ ( 7²7 5²,50) = -2/x
x
з
Also find Euler -Longronze ey's for I and 3
land write them in vector notation for vector
X = (x₂y₂3). Give Jemeterical interpretation what
they tell you.
C). show that Beltrami-identity does not help you
to solve the equation-
d). Let u be an arbitrary increasing for of t. show
that
ƒ [√xx ²)² + (Y²) ²³+ (3³) ³ ] du = √ [] x² + y + z ² ] du
where. x'=dx, Explain what this signifies
geometrically and why this means that one can
assumes without loss of generalify that
| 1 = R along solution of the
|
Euler-longrange equations & -](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5fb4c48-e210-4c5e-a541-160a60a9de22%2Fb7c4b15e-215b-49a4-a9cd-d91928d52275%2Fvt6hqb49_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Day:
Date: //20
A constrained extremisation Problem is expressed
as longsonge-multiplier problem with objective
functional.
I [X³ X] = √ [√x² ² + y² + 3 2 _k (t) (x²+ y² +3²_R²) ]dt
where x = dxc etc. and intereral has appropriate
fixed limitat
with fixed values of Xoy and
7 at the endpoints.
a). Explain what geometric problem is solved fiere and
Is there a local or global constraint.
for Variable x
b)- show that ewler-longronge eq.
takes the form,
d
at
x
√ ( 7²7 5²,50) = -2/x
x
з
Also find Euler -Longronze ey's for I and 3
land write them in vector notation for vector
X = (x₂y₂3). Give Jemeterical interpretation what
they tell you.
C). show that Beltrami-identity does not help you
to solve the equation-
d). Let u be an arbitrary increasing for of t. show
that
ƒ [√xx ²)² + (Y²) ²³+ (3³) ³ ] du = √ [] x² + y + z ² ] du
where. x'=dx, Explain what this signifies
geometrically and why this means that one can
assumes without loss of generalify that
| 1 = R along solution of the
|
Euler-longrange equations & -
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