Wikipedia states baldly that the curves that solve these two completely different optimization problems have the same cycloid shape. No proof is given for the tunnel-through-the-earth problem. On Wed, May 16, 2012 at 10:14 AM, James Aaronson <jamesaaaronson@gmail.com>wrote:
I see no reason why it has to be the same as the brachistochrone. That assumes we're in a uniform gravitational field, whereas the field works differently here; the field at a distance r from the centre of the planet can be given by GM'/r^2, where M' is the mass of planet which is at a distance less than r from the centre.
On Wed, May 16, 2012 at 2:56 PM, Simon Plouffe <simon.plouffe@gmail.com
wrote:
Hello,
I am not certain I understand correctly but isn't this curve the brachistochrone ?
http://en.wikipedia.org/wiki/Brachistochrone_curve
Which is the minimal time curve, is it what you are looking for ?
Or another one with constraint ? : http://en.wikipedia.org/wiki/Tautochrone_curve
Best regards, simon plouffe _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- James _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun