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VariationalCalculus[Weierstrass] - compute the Weierstrass excess function
Calling Sequence
Weierstrass(f, t, x(t), p)
Parameters
f
-
expression in t, x(t), and x'(t)
t
independent variable
x(t)
unknown function (or list of functions)
p
name to use for the vector p[1..n]
Description
The Weierstrass(f, t, x, x(t), p) command computes the Weierstrass excess function
The output is unsimplified. There are many techniques that can be used to simplify the output: factor, collect, combine, or complete the square.
If is positive when is the extremal, except when , the extremal provides a strong local minimum.
The Cauchy-Schwarz inequality can be used to determine the sign of the expression.
Examples
A Lagrange Multiplier Problem (Queen Dido's problem): Find the maximum area enclosed by a curve of length .
See Also
collect, combine, eval, factor, Student[Precalculus][CompleteSquare], VariationalCalculus, VariationalCalculus[EulerLagrange]
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