
2
Constrained variational problems
The boundary values applied in the prior discussion may also be considered
as constraints. The subject of this chapter is to generalize the constraint con-
cept in two senses. The first is to allow more difficult, algebraic boundary
conditions, and the second is to allow constraints imposed on the interior of
the domain as well.
2.1 Algebraic boundary conditions
There is the possibility of defining the boundary condition at one end of the
integral of the variational problem with an algebraic constraint. Let the
x
1
x
0
f(x, y, y
)dx = extremum
variational problem subject to the customary boundary condition
y(x
0
)=y
0
,
on the lower ...