MathGroup Archive 1996

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Simple Pendulum

  • To: mathgroup at
  • Subject: [mg3575] Simple Pendulum
  • From: Christian NEEL <FRVALRFQ at IBMMAIL.COM>
  • Date: Mon, 25 Mar 1996 21:35:24 -0500
  • Sender: owner-wri-mathgroup at

I am in need of the most accurate analytic evaluation of 
the motion solution in a true simple pendulum.

i.e : an analytic solution of the following ODE : 

J Teta''[t] + k Teta'[t] + m g Sin[Teta[t]]==0

Where : J, k, m, g are constants.

Teta (angle) is the unknown function of t

Initial conditions : 	Teta[0]==Teta0, Constant

			Teta'[0]==Omega0, Constant.

I guess that the analytical solution (if existing) could be
expressed in terms of special functions. In the event 
where no explicit solution exist, I am still interested in 
an analytical expression of the boundary between attraction 
bassins in the phase plane (Teta,Teta').

Thank You in Advance



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