Applied Calculus of Variations for Engineers, 2nd Edition

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 ...