Inverted Pendulum
Why Physics Stack Exchange recommends it
Physics Stack Exchange answerers point people to it as a clear, real-world example of a pendulum stabilized in its inverted position by a vibrating pivot.
Recommended by 1 people across 1 different months, 2014 to 2024.
What it is
A short lecture demonstration from Harvard's Natural Sciences Lecture Demonstrations showing a physical pendulum that balances upright when its pivot is driven up and down at about 50 Hz with roughly 1 cm amplitude. The description gives the pendulum's length, mass and rotational inertia and links to a fuller write-up.
What people said
Recommends Manuel Pena · 2020-11 · Physics Stack Exchange · on “Why does ponytail-style hair oscillate horizontally, but not vertically when jogging?”
As @nuclear-hoagie said [LINK] , the ponytail is basically a pendulum, so vibrations up and down are not really possible (or are much more complicated) as the hair would have to elongate itself in order to store the kinetic energy from the hair falling down so it cannot release it later. However the sideways and back and forth vibrations can be maintained almost for free as they do not involve stretching the hair. I guess that you don't see the back and forth vibration for a reason somewhat similar to the up and down case, when the hair stops agains the back it loses all its kinetic energy and cannot continue the vibration. You can look for parametric resonance in vertically vibrated pendulu
Cites docscience · 2014-10 · Physics Stack Exchange · on “Unstable equilibrium in a pendulum”
Maybe in a perfect world with no thermal or atmospheric disturbance (yes simulation) this could happen. Zeno holds true regarding infinite time, but for all practical purposes the bob would appear to get there in a reasonably short time. In the real world control systems engineers accomplish this feat all the time using feedback to overcome the small disturbances mentioned above. Once the bob reaches 12 o'clock, the controls dither the pivot point back and forth to stabilize it. In fact random dither without feedback control can be used to stabilize the inverted pendulum. See an amazing demonstration at Harvard here: [this video]
Cites Cort Ammon · 2024-03 · Physics Stack Exchange · on “Is work done by hinge force always 0?”
Yes, as long as we're only talking about rotation about the axis. As a rather famous counter example, we can look at the inverted pendulum [this video] . In this case, we don't just have rotation about the axis, we also have up and down motion. The up and down motion *can* impart energy. Why this particular motion stabilizes the pendulum is the subject of a control theory course, but at the very least it demonstrates energy being transmitted through a bearing (basically a hinge) through a motion other than rotation about the axis.