Re: Re: Re: Non-Linear pendulum
- To: mathgroup at smc.vnet.net
- Subject: [mg105036] Re: [mg105011] Re: Re: [mg104874] Non-Linear pendulum
- From: "David Park" <djmpark at comcast.net>
- Date: Wed, 18 Nov 2009 07:01:05 -0500 (EST)
- References: <18584294.1258455287758.JavaMail.root@n11>
Alexei, Sometimes one is deriving a function by various Solve routines, or by substitutions and perhaps in multiple steps. If it is a major object of the analysis, then I would prefer to actually SEE the function that results and not have it depend on a chain of previous definitions. And I usually like to have explicit items in graphics statements and not a chain of evaluations. It makes it easier to understand what is happening and debug if there are problems. But it is really a matter of style and preference. David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: Alexei Boulbitch [mailto:Alexei.Boulbitch at iee.lu] Dear David, in your answer to this question (as well as in some other answers) I met the construction: \[Theta][t_] = \[Theta][t] /. s Previously I met constructions like \[Theta][t_] with SetDelayed, rather than with Set. Could you please comment a bit on the use of such a construct with Set? Thank you in advance and best regards, Alexei pendulum = {Line[{{0, 0}, {0, -1}}], Circle[{0, -1.3}, 0.3]}; l = 20; g = 9.81; Clear[\[Theta]]; s = First@ NDSolve[{\[Theta]''[t] == -g/l Sin[\[Theta][t]], \[Theta][0] == Pi/2, \[Theta]'[0] == 0}, \[Theta], {t, 0, 30}] \[Theta][t_] = \[Theta][t] /. S Animate[ Graphics[Rotate[pendulum, \[Theta][t], {0, 0}], PlotRange -> {{-2, 2}, {-2, .5}}], {t, 0, 30}, AnimationRunning -> False] David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ <http://home.comcast.net/%7Edjmpark/> From: Allamarein [mailto:matteo.diplomacy at gmail.com] I'm getting to know Mathematica. I want to compile a code to see the non-linear pendulum behavior. pendulum= {Line[{{0, 0}, {0, -1}}], Circle[{0, -1.3}, 0.3]}; l = 20; g = 9.81; s = NDSolve[ { \[Theta]''[t] == -g /l Sin[\[Theta][t]], \[Theta][0] == Pi/2, \[Theta]'[0] == 0}, \[Theta], {t, 0, 30}]; Animate[ Graphics[Rotate[pendulum, \[Theta[]t], {0, 0}], PlotRange -> {{-2, 2}, {0, -2}}], {t, 0, 30}, AnimationRunning -> False] This code doesn't work. I realized my error is in Rotate argument. If I change this line with: Graphics[Rotate[pendulum, Sin[t], {0, 0}] code runs, but it's not the result (obviously). How can I correct my code, to see the pendulum oscillates with \[Theta] [t] law? -- Alexei Boulbitch, Dr., habil. Senior Scientist IEE S.A. ZAE Weiergewan 11, rue Edmond Reuter L-5326 Contern Luxembourg Phone: +352 2454 2566 Fax: +352 2454 3566 Website: www.iee.lu This e-mail may contain trade secrets or privileged, undisclosed or otherwise confidential information. If you are not the intended recipient and have received this e-mail in error, you are hereby notified that any review, copying or distribution of it is strictly prohibited. Please inform us immediately and destroy the original transmittal from your system. Thank you for your co-operation.