NTNUJAVA Virtual Physics Laboratory
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Information about this web site => Request for physics Simulations => Topic started by: Fu-Kwun Hwang on June 17, 2009, 10:12:40 am

Title: torsional wave
Post by: Fu-Kwun Hwang on June 17, 2009, 10:12:40 am
The fllowing simulation was created due to the following request:
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 $\omega_i=\frac{d c_i}{dt}$

Title: New version of torsional wave
Post by: Fu-Kwun Hwang on April 16, 2010, 11:03:07 am
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.