Editing Inverted pendulum (section)

{{Short description|Pendulum with center of mass above pivot}}
{{More footnotes|date=January 2010}}

[[File:Balancer with wine 3.JPG|thumb|upright=1.2|Balancing cart, a simple robotics system circa 1976. The cart contains a [[servo system]] that monitors the angle of the rod and moves the cart back and forth to keep it upright.]]

An '''inverted pendulum''' is a [[pendulum]] that has its [[center of mass]] above its [[Lever|pivot]] point.  It is [[unstable equilibrium|unstable]] and falls over without additional help. It can be suspended stably in this inverted position by using a [[control system]] to monitor the angle of the pole and move the pivot point horizontally back under the center of mass when it starts to fall over, keeping it balanced.  The inverted pendulum is a classic problem in [[dynamics (mechanics)|dynamics]] and [[control theory]] and is used as a benchmark for testing control strategies.  It is often implemented with the pivot point mounted on a cart that can move horizontally under control of an electronic servo system as shown in the photo; this is called a '''cart and pole''' apparatus.<ref>C.A. Hamilton Union College Senior Project 1966</ref> Most applications limit the pendulum to 1 [[Degrees of freedom (mechanics)|degree of freedom]] by affixing the pole to an [[axis of rotation]]. Whereas a normal pendulum is stable when hanging downward, an inverted pendulum is inherently unstable, and must be actively balanced in order to remain upright; this can be done either by applying a [[torque]] at the pivot point, by moving the pivot point horizontally as part of a [[feedback]] system, changing the rate of rotation of a mass mounted on the pendulum on an axis parallel to the pivot axis and thereby generating a net torque on the pendulum, or by oscillating the pivot point vertically. A simple demonstration of moving the pivot point in a feedback system is achieved by balancing an upturned broomstick on the end of one's finger.

A second type of inverted pendulum is a [[tiltmeter]] for tall structures, which consists of a wire anchored to the bottom of the foundation and attached to a float in a pool of oil at the top of the structure that has devices for measuring movement of the neutral position of the float away from its original position.