Re: Ball Rolling down on Cosh[t] Path
- To: mathgroup at smc.vnet.net
- Subject: [mg36753] Re: Ball Rolling down on Cosh[t] Path
- From: "Borut L" <gollum at email.si>
- Date: Mon, 23 Sep 2002 03:32:50 -0400 (EDT)
- References: <ambv6f$r44$1@smc.vnet.net> <amh3cc$9g3$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
As I derived a generalization for a 3D parameterized curve yesterday, I'd noticed a mistake in my equation posted below, a factor '2' in expression involving x'[t]^2, should be '1'. Since this forum is of an alt. type, I've published the whole notebook at http://www2.arnes.si/~gljpoljane22/math/FallingCurve3D.nb Bye, Borut p.s. A 'fill-the-gap' riddle for those interested in physics lore. Richard Feynman once said: "Science is like _ _ _, sometimes something useful comes out, but that is not the reason why we are doing it." | ... | 1) I'll leave re-deriving equation to you, here is what I've got (just copy | paste it).: | | \!\(getEq[ | f_] := \[IndentingNewLine]\(x''\)[ | t] + \(x'\)[t]\^2\ \(2\ \(f'\)[x[t]]\ \(f''\)[x[t]]\)\/\(1 + | \(f'\ | \)[x[t]]\^2\) + \(g\ \(f'\)[x[t]]\)\/\(1 + \(f'\)[x[t]]\^2\) == 0 /. g -> | 1\) | ...