# Toronto Math Forum

## APM346-2018S => APM346––Home Assignments => Topic started by: Jingxuan Zhang on March 30, 2018, 06:02:18 PM

Title: problem in problem
Post by: Jingxuan Zhang on March 30, 2018, 06:02:18 PM
I assume problem 2.1 of http://www.math.toronto.edu/ivrii/PDE-textbook/Chapter10/S10.P.html intends to ask "Minimizing T" subject to no constrain?
Title: Re: problem in problem
Post by: Victor Ivrii on March 30, 2018, 07:40:01 PM
No constrains affecting L.-E. equations,

(A) but there is a constrain  $u(0)=0$, $u(a)=h$

(B) In fact, one can remove the last constrain.
With (A) we are looking for the fastest slide between two points (so given are horizontal projection and the difference in heights)
With (B) only horizontal projection..

http://mathworld.wolfram.com/BrachistochroneProblem.html (http://mathworld.wolfram.com/BrachistochroneProblem.html)