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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: torsional wave  (Read 9072 times)
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Fu-Kwun Hwang
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on: June 17, 2009, 10:12:40 am » posted from:Taipei,T\'ai-pei,Taiwan

The fllowing simulation was created due to the following request:
Quote
Hello Fu- Kwun Hwang
 
I would like to introduce myself; I am a metalwork sculptor living in Sheffield, England and came across your wonderful animated pendulum simulations on the COLOS website while researching a current project. This project involves the creation of a kinetic artwork based on a human powered 'wave" intended to mimic the effect of the 'Mexican waves' seen in sports stadiums around the world.
 
After seeing your computer simulations I would be very interested in talking to you about your work and hope you could help me with the mathematics of achieving the effect I am trying to create.
 
My own background is as an artist and metalworker and although I do not have a science back ground I enjoy the application of science in my art.
 
 I have made a 1:20 Scale model and achieved the 'Wave' effect I wanted with the model suspended in air. To progress things further I am trying to find somebody who can help me with the mathematics so i can produce working drawings and create kinetic artwork for a freshwater pool in a Lancashire quarry in the UK; (For further information - see attached file - echofly 2.pdf )

I understand this may not be your normal line of work, but if it is of interest?; I can send you more information and I would welcome an opportunity to discuss it with you in more detail.
 
Kind regards Robin Dobson
-*-

The angle for each one is c_i, which is a function of time t.
The restore torque is assume to be k*(c_{i+1}-c_i)-k*(c_i-c_{i-1})=k*(c_{i+1}+c_{i-1}-2*c_i),
The torque due to gravitation force is m*g*h*\sin(c_i)/I, where  I is the moment of rotational inertia.
A damping torque -b*\omega_i is also added, where \omega_i=\frac{d c_i}{dt}

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Fu-Kwun Hwang
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Reply #1 on: April 16, 2010, 11:03:07 am » posted from:Taipei,T\'ai-pei,Taiwan

Here is another version of torsional wave (demostration)

Change the c angle with slider and watch how wave propagate.
The slider for i can be used to change angle for i-th element.

The force acting on each element is
F_i= K* c_i + K_ij * (c_{i+1}-c_i)+K_ij (c_i-c_{i-1})-b*\omega_i
where c_i is the i-th angle, \omega_i is the angular velocity, b is damping constant, K_ij represent interaction between elements.

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Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
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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An interaction between two opposites produces a unique outcome. ..."Jules Henri Poincare(1854-1912, One of France's greatest mathematicians)"
 
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