Thanks for your help! :) I've discovered that these kinds of constraints are called "non-holonomic", which has in turn improved my research on the matter. That, coupled with your link on PMP, should be sufficient for now. Thanks again!
y(x) = h(x) totally seems to be a candidate solution, but to me this doesn't imply that you flatten everything in your path out. Rather, you'd simply follow the contour of the given terrain exactly, neither removing nor adding dirt. It would minimize cost at zero dollars, assuming the...
Looks like you applied L'Hopitals rule right to me - :)
When you say you're not sure what "type" it is, I'm assuming you mean what kind of indeterminate form? If you look at the function in your limit, actually evaluated at the limit value (x = 0), what kind of form is it? Surely not infinity...
[SOLVED] Variational calculus with bounded derivative constraints
After learning about the calculus of variations and optimal control for a bit this semester, I've decided to tackle a "simple" (in the words of my professor) problem meant to illustrate a simplified example of highway...
Hi! I'm in a mathematical ecology class and we're working with delta sequences.
I'm trying to show that
delta_n(x) = n if |x| <= 1/2n
= 0 if |x| > 1/2n
is a delta sequence.
----Definition of a delta sequence---------------------------------------
Suppose...