Applied Calculus of Variations for Engineers, 2nd Edition

54 Applied calculus of variations for engineers

and

y



− y + z =0.

The elimination of the Lagrange multiplier results in the system of

y − z + z



=0,

and

y



− y + z =0,

whose solution follows from classical calculus.

4.4 Linearization of second order problems

It is very common in engineering practice that the highest derivative of interest

is of second order. Accelerations in engineering analysis of motion, curvature

in description of space curves, and other important application concepts are

tied to the second derivative.

This specific case of quadratic problems may be reverted to a linear prob-

lem involving two functions. Consider

I(y)=



x

1

x

0

f(x, y, y



,y

