Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.
|
|
cdj
Posts:
77
Registered:
12/7/04
|
|
What counts as "enough variations"?
Posted:
May 21, 2003 9:03 PM
|
|
Hi all,
Ok, this has bugged me for long enough -
Almost every book I've seen on the calculus of variations says
something to the effect of "as long as there are 'enough' variations
to determine a solution [to the EL equation(s) or to the variational
problem itself]."
What does this mean?
I am perfectly familiar with the fact that for problems of the simple
and unconstrained variety, the vanishing-of-the-1st-variation
necessary condition, one assumes that one is working with a linear
space's worth of variations. But this doesn't smell like what the
books are talking about.
Rather, it seems (to me at least) as tho the books say things of the
above sort in rather in the sense of "as long as there are enough
equations to determine a solution to this linear system", or "as long
as there are enough initial conditions given to determine a unique
solution to this ODE system".
Can anyone give me a good descrition of what these books are talking
about?
(Sorry I don't have one of these books at hand to quote directly from.
I'll get one, if necessary...)
thanks for any enlightenment,
cdj
|
|
|
|
