Variational Problems of Conditional Extrema

Abstract

The variational problems encountered in the natural sciences and engineering technology, sometimes require that the extremal function in addition to satisfying the given boundary conditions, also satisfies certain additional conditions, this is the condition extremal problems for a functional. The extremum obtained by a functional in satisfying some additional conditions is called the conditional extremum. Attaching some constraint conditions to the function that a functional depends on to find the extremal problems of the functional is called the variational problem of conditional extremum. The conditional extremum of functional with holonomic constraint, differential constraint and isoperimetric problem will be discussed in this chapter, and the extremal problems the simple mixed type functional are discussed.