Sure, grhodes actually showed you how to do this when he was talking about damping. Just modify the torque (or angluar acceleration) to include more forces than gravity into the equation. To let the user control the swing with a paddle you could simply add a value to the torque when the paddle is in one direction an subtract the same value when in the other.

try linearisation ( spelling ??? ) its a classical example in theory for a non linear system solving ( the pendulum )

Of course, i am being very slow, thankyou both.

Okay now I have

m*l*l*theta_double_dot + friction * theta_dot + m*g*l*sin theta = 0 but how do i solve it?

Numerical methods, since the equation that you just presented is more complex than the one originally proposed. Look for more numeric integration methods and see what you can find, since I haven''t implemented any of these systems myself.

Brendan

The simplest approach is Euler integration, like grhodes described above. Starting with theta(t0), theta_dot(t0), you can calculate theta_double_dot(t0). Next, approximate theta_dot(t0+dt) = theta_dot(t0) + theta_double_dot(t0)*dt, and theta(t0+dt) = theta(t0) + theta_dot(t0)*dt. Smaller dt will give better approximation. Repeat until you reach the wanted time t = t0+n*dt.

The equations of motion for a pendulum can be expressed in terms of elliptic functins (sn, cn etc). Surely there are some decent libraries to compute them out there.

quote:

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Original post by v71
try linearisation ( spelling ??? ) its a classical example in theory for a non linear system solving ( the pendulum )

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Yes, but Keem did start out with a linearized solution. The linearized solution to the pendulum problem cannot model a pendulum that rotates fully over-the-top in some cases.

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

quote:

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Original post by sQuid
The equations of motion for a pendulum can be expressed in terms of elliptic functins (sn, cn etc). Surely there are some decent libraries to compute them out there.

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Those are the linearized solutions, which, as discussed through this thread, cannot model the behavior that Keem desires (pendulum that not only oscillates about its equilibrium point, but also can be forced to rotate fully 360 degrees).

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

Could you not treat the problem as a circular motion problem?

the speed at any point on the path is then
v^2 = u^2 - 2gr(1 - cos theta)

where u is the initial speed of the pendulum and r is the radius(length of rod).

This equation is derived using conservation of energy principles. It can be possible to determine if the pendulum goes over the top if the following condition is met:

u^2 > 4gr

If this is not the case then the maximum angle obtained can be found by setting v = 0 in the top equation.