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Tautochonous oscillation physics simulation

• To: mathgroup at smc.vnet.net
• Subject: [mg71354] Tautochonous oscillation physics simulation
• From: "Narasimham" <mathma18 at hotmail.com>
• Date: Wed, 15 Nov 2006 06:45:21 -0500 (EST)

After seeing David Park's mechanics/physics program of elastic
collisions simulation. Why not model the tautochronous oscillations of
a particle on a cycloid of same time irrespective of height at start?
The dynamics ordinary differential equation has to be slightly modified
from energy/torque considerations of a particle of a non-linear
pendulum:

th''[t] + kappa * g * th[t] = 0 where th is normal-vertical direction
angle,kappa is cycloid curvature, with kappa*normal length =1/2
etc.properties.Position,speed and acceleration can be computed and
animated.

It could be fun watching the dot going up and down the cycloid bowl, a
classical problem that engaged Huygens and Bernoulli, now using
Mathematica. 

Regards
Narasimham