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Applied Calculus of Variations for Engineers, 2nd Edition
book

Applied Calculus of Variations for Engineers, 2nd Edition

by Louis Komzsik
June 2014
Intermediate to advanced content levelIntermediate to advanced
233 pages
5h 42m
English
CRC Press
Content preview from Applied Calculus of Variations for Engineers, 2nd Edition
30 Applied calculus of variations for engineers
First we separate the variables
dy = ±
x c
1
λ
2
(x c
1
)
2
dx,
and integrate again to produce
y(x)=±
λ
2
(x c
1
)
2
+ c
2
.
It is easy to reorder this into
(x c
1
)
2
+(y c
2
)
2
= λ
2
,
which is the equation of a circle. Since the two given points are on the x axis,
the center of the circle must lie on the perpendicular bisector of the chord,
which implies that
c
1
=
x
0
+ x
1
2
.
To solve for the value of the Lagrange multiplier and the other constant, we
consider that the circular arc between the two points is the given length:
L = λθ,
where θ is the angle of the arc. The angle is related to the remaining constant
as
θ
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Publisher Resources

ISBN: 9781482253597