June 2014
Intermediate to advanced
233 pages
5h 42m
English
Content preview from Applied Calculus of Variations for Engineers, 2nd Edition
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Multivariate functionals 47
were only temporal, the second integral is only zero when
∂f
∂u
x
dy
ds
−
∂
∂u
y
dx
ds
=0,
on the boundary ∂D. This is the constraint of the variational problem. This
result will be utilized in Chapter 11 to solve the elastic membrane problem.
The case of functions with four independent variables such as
u(x, y, z, t)
will also be discussed in Chapter 12 in connection with elasticity problems in
solids.
The generalization of the process to even more independent variables is al-
gebraically straightforward. Generalization to more spatial coordinates is not
very frequent, although in some manufacturing applications five-dimensional
hyper-spaces ...
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