Instability of free rigid body rotation about middle axis

  • #1
Hi everyone, I was recently talking to someone with a non-maths background about rotational stability, in particular how rotation is stable around the largest and smallest principal moments but not the intermediate one. He asked me if there was any 'obvious' reason for this, but one didn't spring to mind.

Obviously to anyone with a mathematical background you would tell them to write down Euler's equations and linearise them for a small perturbation. But I was curious if someone knew of any physical reason which would enable explanation to someone without a maths background.
 

Answers and Replies

  • #2
A.T.
Science Advisor
11,465
2,828
Obviously to anyone with a mathematical background you would tell them to write down Euler's equations and linearise them for a small perturbation. But I was curious if someone knew of any physical reason which would enable explanation to someone without a maths background.
Can't one explain the small perturbation without math, using a simple body, like two masses connected with a rod.
 
  • #3
Meir Achuz
Science Advisor
Homework Helper
Gold Member
3,540
118
That is why we use math.
 
  • Like
Likes vanhees71
  • #4
FactChecker
Science Advisor
Gold Member
6,760
2,773
Can't one explain the small perturbation without math, using a simple body, like two masses connected with a rod.
I tried thinking along those lines, but I was getting the wrong intuitive answer. It is treacherous.

Here is an interesting approach that is more geometric (starting at ~ 1:15) than algebraic. But there is still math graphing involved.
NOTE: This youtube video is a little careless. Both surfaces are ellipsoids. The intersections of the surfaces retain the significant characteristics that are needed to make the main point.. You can visualize the axes being scaled so that one of the ellipsoids is a sphere.
 
Last edited:
  • Like
Likes Jack Davies
  • #5
A.T.
Science Advisor
11,465
2,828
I tried thinking along those lines, but I was getting the wrong intuitive answer. It is treacherous.

Here is an interesting approach that is more geometric (starting at ~ 1:15) than algebraic. But there is still math graphing involved.


Here is more visualization of the geometric approach:

 
  • Like
Likes Jack Davies and FactChecker

Related Threads on Instability of free rigid body rotation about middle axis

Replies
10
Views
2K
Replies
3
Views
7K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
3
Views
598
T
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
0
Views
3K
  • Last Post
Replies
3
Views
2K
Top