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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
42 Applied calculus of variations for engineers
-3
-2
-1
0
1
2
3
-3
-2
-1
0
1
2
3
-30
-20
-10
0
10
20
30
FIGURE 3.1 Saddle surface
the equation.
When a minimal surface is sought in a parametric form
r
= x(u, v)i + y(u, v)j + z(u, v)k.
the variational problem becomes
I(r
)=

D
EF G
2
dA,
where the so-called first fundamental quantities are defined as
E(u, v)=(r
u
)
2
,
F (u, v)=r
u
r
v
,
and
G(u, v)=(r
v
)
2
.
The solution may be obtained from the differential equation
∂u
Fr
u
Gr
v
EF G
2
+
∂v
Er
v
Gr
u
EF G
2
=0.
Multivariate functionals 43
Finding minimal surfaces for special
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Publisher Resources

ISBN: 9781482253597