Inverted Pendulum: Relate Force to Angle/Displacement?

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SUMMARY

The discussion focuses on the dynamics of an inverted pendulum, specifically how to relate the magnitude of an applied force to the angle (theta) or displacement of the pendulum's end. The critical point of interest is when the pendulum passes the vertical, leading to a loss of stability. A suggestion is made to explore the control algorithms used in the Segway personal transport, which operates on similar principles of inverted pendulum dynamics.

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paton51
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Im considering a problem were an inverted pendulum is resting against a ledge an an angle theta from the horizontal. A force is applied to the end causing it to move, This force is dynamic and decrease as the angle increases. The critical point is when the pendulum passes the vertical and cannot return to its resting point falls to the other side.

Does anyone know how i can relate the magnitude of the force to either the angle or displacement of the end of the pendulum?

suggestions welcome.
thanks
 
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I would look around the net and see if you can find any information on the control algorithm used by the Segway personal transport. That is essentially an inverted pendulum.
 

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