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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
116 Applied calculus of variations for engineers
Γ
2
12
=
EG
u
FE
v
2(EG F
2
)
,
and
Γ
2
22
=
EG
v
2FF
v
+ FG
u
2(EG F
2
)
.
These formulae all require that
EG F
2
=0
which is true when a parameterization is regular.
8.2.1 Geodesics of surfaces of revolution
Another practically important special case is represented by surfaces of revo-
lution. Their generic description may be of the form
x = ucos(v),
y = usin(v),
and
z = f (u).
Here the last equation describes the meridian curve generating the surface.
The first order fundamental terms are
E =1+f
2
(u),
F =0,
and
G = u
2
.
The solution following the discussion in Section 8.1 becomes
v = c
1
1+f
2
(u)
u
u
2
c
2
1
du + c
2
.
A simple sub-case ...
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Publisher Resources

ISBN: 9781482253597