High School Intermediate Axis Theorem - Intuitive Explanation

Click For Summary
The discussion focuses on the Intermediate Axis Theorem, particularly the instability of rotation about the middle axis. It highlights that examining a surface of fixed energy reveals six equilibria in three pairs, with the middle axis exhibiting saddle points, leading to instability. The "flipping" phenomenon observed in simulations corresponds to movement near a heteroclinic cycle between these saddle points. The conversation references previous videos and a Veritasium post for additional context. Overall, the thread emphasizes the dynamics of rotational stability and energy conservation in relation to the theorem.
A.T.
Science Advisor
Messages
13,072
Reaction score
4,076
A simulation/animation/explanation based on the inertial frame only:

The previous videos referenced there are here:

See also this post for context on the Veritasium video: https://mathoverflow.net/a/82020

Note to mods: The previous thread is not open anymore so I opened a new one. Feel free to merge them.
 
Last edited:
Reply
  • Like
Likes Lnewqban, Filip Larsen and BvU
Physics news on Phys.org
Here one of the more abstract approaches based on energy/momentum conservation. Unfortunately not much explanation in the video, and just a short description:



Robert Ghrist said:
Why is rotation about the middle axis unstable? If you examine a surface of fixed energy and look at the dynamics, you get six equilibria in three pairs -- rotation about each axis CW and CCW. These equilibria are centers for the longest and shortest axes. But for the middle axis -- the equilibria are saddles! The "flipping" seen in the previous video corresponds to traveling close to a heteroclinic cycle between saddle points.
 

Thread 'Reference frames, center of rotation, etc'

Topic about reference frames, center of rotation, postion of origin etc Comoving ref. frame is frame that is attached to moving object, does that mean, in that frame translation and rotation of object is zero, because origin and axes(x,y,z) are fixed to object? Is it same if you place origin of frame at object center of mass or at object tail? What type of comoving frame exist? What is lab frame? If we talk about center of rotation do we always need to specified from what frame we observe?
View full post »

Similar threads

Undergrad Intermediate Axis Theorem - Intuitive Explanation
  • · Replies 9 ·
Replies
9
Views
6K
High School My paraphrased explanation of the Twin Paradox
  • · Replies 24 ·
Replies
24
Views
4K
Undergrad Gamma - A Minkowski Spacetime Diagram Generator
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Atmospheric Density vs Altitude in an O'Neil Cylinder
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Request for Input: 2D Minkowski Spacetime Diagram Generator
  • · Replies 6 ·
Replies
6
Views
3K
A graphical explanation of Special Relativity
  • · Replies 5 ·
Replies
5
Views
4K
Countdown to Doom Release: Revisit the Original and Celebrate with Easter Eggs
  • · Replies 14 ·
Replies
14
Views
5K
Redesigning Mathematics Curriculum, thoughts?
  • · Replies 65 ·
3
Replies
65
Views
11K
Schools Skipping Straight to Grad School (don't laugh)
  • · Replies 66 ·
3
Replies
66
Views
15K
Modified Twin Paradox. (Experts required).
  • · Replies 23 ·
Replies
23
Views
5K