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MathGroup Archive 2002

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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\)
| ...



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