Editing Inverted pendulum (section)

==Examples==
Arguably the most prevalent example of a stabilized inverted pendulum is a [[human being]].  A person standing upright acts as an inverted pendulum with their feet as the pivot, and without constant small muscular adjustments would fall over.  The human nervous system contains an unconscious [[feedback]] [[control system]], the [[sense of balance]] or [[righting reflex]], that uses [[proprioceptive]] input from the eyes, muscles and joints, and orientation input from the [[vestibular system]] consisting of the three [[semicircular canals]] in the [[inner ear]], and two [[otolith]] organs, to make continual small adjustments to the skeletal muscles to keep us standing upright.  Walking, running, or balancing on one leg puts additional demands on this system.  Certain diseases and alcohol or drug intoxication can interfere with this reflex, causing [[dizziness]] and [[disequilibrium (medicine)|disequilibration]], an inability to stand upright.  A [[field sobriety test]] used by police to test drivers for the influence of alcohol or drugs, tests this reflex for impairment.

Some simple examples include balancing brooms or meter sticks by hand. 
 
The inverted pendulum has been employed in various devices and trying to balance an inverted pendulum presents a unique engineering problem for researchers.<ref>{{Cite web |url=http://csuchico-dspace.calstate.edu/bitstream/handle/10211.4/145/4%2022%2009%20Jose%20Miranda.pdf?sequence=1 |title=Archived copy |access-date=2012-05-01 |archive-url=https://web.archive.org/web/20160304210530/http://csuchico-dspace.calstate.edu/bitstream/handle/10211.4/145/4%2022%2009%20Jose%20Miranda.pdf?sequence=1 |archive-date=2016-03-04 |url-status=dead }}</ref> The inverted pendulum was a central component in the design of several early [[seismometer]]s due to its inherent instability resulting in a measurable response to any disturbance.<ref>{{cite web| url = https://earthquake.usgs.gov/learn/topics/seismology/history/part12.php| url-status = dead| archive-url = https://web.archive.org/web/20091128150331/http://earthquake.usgs.gov/learn/topics/seismology/history/part12.php| archive-date = 2009-11-28| title = The Early History of Seismometry (to 1900)}}</ref>

The inverted pendulum model has been used in some recent [[personal transporter]]s, such as the two-wheeled [[self-balancing scooter]]s and single-wheeled [[electric unicycle]]s. These devices are kinematically unstable and use an electronic feedback [[servo system]] to keep them upright.

Swinging a pendulum on a cart into its inverted pendulum state is considered a traditional [[optimal control]] toy problem/benchmark.<ref>{{Cite web|url=https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-832-underactuated-robotics-spring-2009/readings/MIT6_832s09_read_ch03.pdf|title=The Acrobot and Cart-Pole}}</ref><ref>{{Cite web|url=http://www.cs.huji.ac.il/~ai/projects/2017/learning/Cart-pole-swing-up/|title=Cart-Pole Swing-Up|website=www.cs.huji.ac.il|access-date=2019-08-19}}</ref>
[[File:Cart-pole swing up.gif|thumb|Trajectory of a fixed time cartpole swing up that minimizes the force squared]]