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An interaction between two opposites produces a unique outcome. ..."Jules Henri Poincare(1854-1912, One of France's greatest mathematicians)"

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 Author Topic: particle moving on top of a torus  (Read 11010 times) 0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).
mako
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 « Embed this message on: June 13, 2009, 09:16:04 am » posted from:BogotÃ¡,Cundinamarca,Colombia

hello
great job tnx

plz, I need a  3d simulation of a particle moving on top of a torus surface, the particle can move over any hemisphere  (subject to a gravitational field) and parallel of the toroid like a simple pendulum able to spin around depending on the total energy.
THe particle has no friction.

I need to set the mass, potential energy, kinetic energy (for both angles gamma and beta), value, and if possible the axial and ring radius.

plz I need the graphs of potential energy vs beta, and a field diagram for momentum beta vs beta

THe purpose of this animation is educational for students to interact with values in order to visualize the movement and describe some situations that can arise

this is for BOgota COlombia,
Tnx so much

 ToroideCoordenado copiar.jpg (17.54 KB, 322x206 - viewed 485 times.) Logged
Fu-Kwun Hwang
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 « Embed this message Reply #1 on: June 13, 2009, 10:18:42 am » posted from:Taipei,T\'ai-pei,Taiwan

Do you mean a particle is restricted to move on a torus surface (inside a torus and always in contact with the surface)?

What is the interaction force between particle and the torus surface? Normal force ?
or Is there another force to keep particle always in contact with the torus surface (it might fall down due to gravity).

Assume the larger radius is R, and smaller radius is r for the torus.
Does $z=r \sin\beta$, and $\tan\gamma=y/x$ in your case?
I do not understand the meaning of $\alpha$ in the attached picture.
Your problem might be similar to a circular motion in vertical direction , plus a constant angular speed rotational motion (angular momentum is conserved).
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diavila
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 « Embed this message Reply #2 on: June 13, 2009, 09:24:50 pm » posted from:BogotÃ¡,Cundinamarca,Colombia

Do you mean a particle is restricted to move on a torus surface (inside a torus and always in contact with the surface)?
The particle is always in contact with the surface, ie never change toroid.
What is the interaction force between particle and the torus surface? Normal force ?
Only normal force
or Is there another force to keep particle always in contact with the torus surface (it might fall down due to gravity).

Assume the larger radius is R, and smaller radius is r for the torus.
Does $z=r \sin\beta$, and $\tan\gamma=y/x$ in your case?
Yes
I do not understand the meaning of $\alpha$ in the attached picture.
The largest radio is called $c$ and the radius of the ring is not called $\alpha$, this is called $a$.
Your problem might be similar to a circular motion in vertical direction , plus a constant angular speed rotational motion (angular momentum is conserved).
If something similar. The treatment of the problem has been with the Hamilton's mechanics. I can send a pdf file, the bad is that this in Spanish.
Thanks from Bogotá, Colombia
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Fu-Kwun Hwang
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 « Embed this message Reply #3 on: June 13, 2009, 10:48:05 pm » posted from:Taipei,T\'ai-pei,Taiwan

If normal force is the only interaction between particel and torus, there is a minimum velocity to keep the particle always attached to the torus surface.
The coordinate of the particle is

$x=(R+ r\cos\theta) \cos \phi$
$y=(R+ r\cos\theta) \sin \phi$
$z=r \sin\phi$

Due to symmetry, $\frac{d\phi}{dt}=\frac{2 \pi}{T}$ is a constant, and due to gravity $\frac{d^2\theta}{dt^2}=-\frac{g\cos\theta}{r}$

You can adjust mass m (no effect on the motion), both radius R and r with slider.

Embed a running copy of this simulation

Embed a running copy link(show simulation in a popuped window)
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Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop. This work is licensed under a Creative Commons Attribution 2.5 Taiwan License
• Please feel free to post your ideas about how to use the simulation for better teaching and learning.
• Post questions to be asked to help students to think, to explore.
• Upload worksheets as attached files to share with more users.
Let's work together. We can help more users understand physics conceptually and enjoy the fun of learning physics!
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bradcapo2
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 « Embed this message Reply #4 on: July 27, 2009, 08:10:26 am » posted from:Hanoi,Dac Lac,Vietnam

I am not so knowledgeable about this matter. So i have to learn it. Thanks for the post.

-*-

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An interaction between two opposites produces a unique outcome. ..."Jules Henri Poincare(1854-1912, One of France's greatest mathematicians)"
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