Dec 19, 2023 · Physics-based simulation of a vibrating pendulum with a pivot point is shaking rapidly up and down. Surprisingly, the position with the pendulum being vertically upright is stable, so this is also known as the inverted pendulum.

An inverted pendulum in which the pivot is oscillated rapidly up and down can be stable in the inverted position. This is called Kapitza's pendulum , after Russian physicist Pyotr Kapitza who first analysed it.

The objective is to develop a control model or a control loop to generally achieve stability. In our case, balance the upside down pendulum. There are two main types of control loops: open loop control and closed loop control.

Our model for the inverted pendulum is shown in Figure xxx. Assuming for the moment that the pendulum leg has zero mass, then gravity exerts a force. where Fperp is the component of the gravitational force perpendicular to the leg, and M is the mass at the end of the leg.

A physical pendulum finds stability in its inverted position when driven at the proper frequency and amplitude combination. How it works The physical pendulum is a 45 cm x 2 cm x 6 mm (1/4") strip mounted on a ball-bearing pivot and can rotate 360 degrees.

In the present problem, this amounts to reversing the force of gravity, making it pull the pendulum up. But an upside-down pendulum is just another pendulum. Therefore the function sn(it;k) must also be periodic as a function of t. This suggests that sn(z;k), as a function of z 2 C, is periodic in both the real and imaginary directions. And it ...

Balancing a pencil on the tip of your finger is difficult, isn't it? But to stabilize a rigid pendulum in the upside-down position is easy! You don't need sophisticated controlling technology. You only need a simple and fast motor moving the suspension point of the pendulum periodically up and down! If you don't believe me, try it in the lab!

Model a pendulum by a mass m that is connected to a hinge by an idealized rod that is massless and of fixed length l. Invert the pendulum and shake the pivot point vertically. Suppose that at time t, the location of the pivot point is x = 0, y = h(t). Denote by θ …

This demonstration illustrates that one can stabilize an upside down pendulum by shaking it vertically. If a pendulum consists of a mass connected to a frictionless hinge by an idealized rod of length L, then the angle θ between the rod and vertical obeys the differential equation.

Specifically, the design criteria are that the pendulum return to its upright position within 5 seconds and that the pendulum never move more than 0.05 radians away from vertical after being disturbed by an impulse of magnitude 1 Nsec.