torsional wave

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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