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