[Date Index]
[Thread Index]
[Author Index]
Re: Ball Rolling down on Cosh[t] Path
 To: mathgroup at smc.vnet.net
 Subject: [mg36730] Re: Ball Rolling down on Cosh[t] Path
 From: "Borut L" <gollum at email.si>
 Date: Sat, 21 Sep 2002 02:21:54 0400 (EDT)
 References: <ambv6f$r44$1@smc.vnet.net>
 Sender: ownerwrimathgroup at wolfram.com
Having noticed your statement " ... BEYOND MY MEANS " I thing you aren't yet
familiar with Lagrangian formalism. It's quite easy to derive a general
equation of motion for a point mass, subjected to gravity and to moving on a
curve f = y(x) (i.e. f = Cosh[#]&).
1) I'll leave rederiving 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\)
2) Next, you integrate it .:
getSol[f_, x0_] :=
Module[{tStop},
NDSolve[{getEq[f], x[0] == x0, x'[0] == 0}
, x
, {t, 0, 10}
, MaxStepSize > 1/100
, StoppingTest :> If[x0 < 0, x > 0, x < 0]
] // First
]
3) Here follows animation code, specially for linear versus cosh case, apply
my initial conditions (below)
makeDuo[f_, g_, x0_, fpt_] :=
Module[{
solf = getSol[f, x0],
solg = getSol[g, x0],
tf, tg, maxT, minT
},
tf = solf[[1, 2, 1, 1, 2]];
tg = solg[[1, 2, 1, 1, 2]];
maxT = Max[{tf, tg}];
minT = Min[{tf, tg}];
Do[
Plot[{f@x, g@x}
, {x, 0, x0}
, AspectRatio > Automatic
, Frame > True
, Axes > False
, Epilog > {
AbsolutePointSize[10],
Hue[0], Point[{x[t], f@x[t]} /. solf],
Hue[.6], Point[{x[t], g@x[t]} /. solg]
}
]
, {t, 0, minT, minT/fpt}
]
]
4) My initial conditions. In my opinion, you weren't true on this. Saying "
STARTING FROM THE SAME HEIGHT " is not enough  you should specify x as
well, thus specifing starting POINT and not just height y.
makeDuo[(Cosh[1.]  1) # &, Cosh[#]  1 &, 1, 23]
Feel free to modify the code, it should be easy.
bye,
Borut
<Matthias.Bode at oppenheim.de> wrote in message
news:ambv6f$r44$1 at smc.vnet.net...
 Dear Colleagues,

 I intend to make an animation in which

 ball A rolls down on an inclined plane from the left whilst

 ball B  starting from the same height  rolls down Cosh[t]'s path from
the
 right.

 xaxis is time t, yaxis is height h.

 Ball A is fine; ball B  which should arrive at h=0 before A  is beyond
my
 means.

 Thank you for your consideration,

 Matthias Bode
 Sal. Oppenheim jr. & Cie. KGaA
 Koenigsberger Strasse 29
 D60487 Frankfurt am Main
 GERMANY
 Tel.: +49(0)69 71 34 53 80
 Mobile: +49(0)172 6 74 95 77
 Fax: +49(0)69 71 34 95 380
 Email: matthias.bode at oppenheim.de
 Internet: http://www.oppenheim.de


Prev by Date:
RE: Re: buildin commutativity
Next by Date:
RE: How to display package contents?
Previous by thread:
Re: Ball Rolling down on Cosh[t] Path
Next by thread:
RE: Re: Ball Rolling down on Cosh[t] Path
 