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작성자짱깨 조회 4회 작성일 2021-01-27 12:03:14 댓글 0

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The Bizarre Behavior of Rotating Bodies, Explained

Spinning objects have strange instabilities known as The Dzhanibekov Effect or Tennis Racket Theorem - this video offers an intuitive explanation.
Part of this video was sponsored by LastPass, click here to find out more: https://ve42.co/LP

References:
Prof. Terry Tao's Math Overflow Explanation: https://ve42.co/Tao

The Twisting Tennis Racket
Ashbaugh, M.S., Chicone, C.C. \u0026 Cushman, R.H. J Dyn Diff Equat (1991) 3: 67. https://doi.org/10.1007/BF01049489

Janibekov’s effect and the laws of mechanics
Petrov, A.G. \u0026 Volodin, S.E. Dokl. Phys. (2013) 58: 349. https://doi.org/10.1134/S1028335813080041

Tumbling Asteroids
Prave et al. https://doi.org/10.1016/j.icarus.2004.07.021

The Exact Computation of the Free Rigid Body Motion and Its Use in Splitting Methods
SIAM J. Sci. Comput., 30(4), 2084–2112
E. Celledoni, F. Fassò, N. Säfström, and A. Zanna
https://doi.org/10.1137/070704393

Animations by Iván Tello and Isaac Frame

Special thanks to people who discussed this video with me:
Astronaut Don Pettit
Henry Reich of MinutePhysics
Grant Sanderson of 3blue1brown
Vert Dider (Russian YouTube channel)

Below is a further discussion by Henry Reich that I think helps summarize why axes 1 and 3 are generally stable while axis 2 is not:

In general, you might imagine that because the object can rotate in a bunch of different directions, the components of energy and momentum could be free to change while keeping the total momentum constant.

However, in the case of axis 1, the kinetic energy is the highest possible for a given angular momentum, and in the case of axis 3, the kinetic energy is the lowest possible for a given angular momentum (which can be easily shown from conservation of energy and momentum equations, and is also fairly intuitive from the fact that kinetic energy is proportional to velocity squared, while momentum is proportional to velocity - so in the case of axis 1, the smaller masses will have to be spinning faster for a given momentum, and will thus have more energy, and vice versa for axis 3 where all the masses are spinning: the energy will be lowest). In fact, this is a strict inequality - if the energy is highest possible, there are no other possible combinations of momenta other than L2=L3=0, and vice versa for if the energy is the lowest possible.

Because of this, in the case of axis 1 the energy is so high that there simply aren't any other possible combinations of angular momentum components L1, L2 and L3 - the object would have to lose energy in order to spin differently. And in the case of axis 3, the energy is so low that there likewise is no way for the object to be rotating other than purely around axis 3 - it would have to gain energy. However, there's no such constraint for axis 2, since the energy is somewhere in between the min and max possible. This, together with the centrifugal effects, means that the components of momentum DO change.

Rotation Guide for Rocket League

Rotation is one of the hardest skills to understand in Rocket League. This is a Rotation Guide. This video covers how to rotate in any game mode. Rotation can be a skill that takes you to higher ranks without much practice or change. However mastering rotation can take thousands of hours of play time to fully understand how you need to rotate and how rotation works most efficiently




Rotation poem:
If you don't know where to be
and you don't know where to go
make sure that you rotate
all the way to back post
Rotation can be tricky
Rotation can be hard
if you do not pay attention
you will bump into other cars
Running out of boost?
Are you too far away
Rotate over pads
so you can stay close to the play
ROTATION!


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Rotating Moon from LRO

Credit: NASA, Arizona State U., NASA

Details: http://lroc.sese.asu.edu/news/index.php?/archives/790-A-Unique-View-Of-The-Moon.html

Details: https://apod.nasa.gov/apod/ap130916.html
and https://apod.nasa.gov/apod/ap180318.html


APOD Caption

No one, presently, sees the Moon rotate like this. That's because the Earth's moon is tidally locked to the Earth, showing us only one side. Given modern digital technology, however, combined with many detailed images returned by the Lunar Reconnaissance Orbiter (LRO), a high resolution virtual Moon rotation movie has now been composed. The above time-lapse video starts with the standard Earth view of the Moon. Quickly, though, Mare Orientale, a large crater with a dark center that is difficult to see from the Earth, rotates into view just below the equator. From an entire lunar month condensed into 24 seconds, the video clearly shows that the Earth side of the Moon contains an abundance of dark lunar maria, while the lunar far side is dominated by bright lunar highlands. Currently, over 20 new missions to the Moon are under active development from four different countries, most of which have expected launch dates either this year or next.

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