Why Do Spinning Tops Behave Differently in Theory and Reality?

  • Context: Graduate 
  • Thread starter Thread starter James_Frogan
  • Start date Start date
  • Tags Tags
    Spinning
Click For Summary
SUMMARY

The discussion focuses on the behavior of spinning tops, particularly the discrepancies between theoretical predictions based on Lagrange solutions and observed real-world behavior. Users note that while theoretical models suggest looping or sinusoidal motions, actual spinning tops exhibit steady precession with Euler's angle theta remaining constant. Additionally, there is confusion regarding the Kowalevsky top and its practical applications versus theoretical constructs, with a request for beginner-friendly resources on Hamiltonian mechanics.

PREREQUISITES
  • Understanding of Lagrange solutions for spinning tops
  • Familiarity with Euler angles and their significance in rotational dynamics
  • Basic knowledge of Hamiltonian mechanics
  • Ability to interpret equations of motion in classical mechanics
NEXT STEPS
  • Research Hamiltonian mechanics for beginners to clarify its principles
  • Explore the practical applications of the Kowalevsky top in physics
  • Investigate the differences between theoretical and experimental observations of spinning tops
  • Watch educational videos on the dynamics of spinning tops to visualize their behavior
USEFUL FOR

Physics students, mechanical engineers, and hobbyists interested in classical mechanics and the dynamics of spinning objects.

James_Frogan
Messages
27
Reaction score
0
I'm beginning to read about spinning tops and in particular, the Lagrange solutions for these tops.

1) When I solve the equations of motion for these tops (acting under gravity), the resultant motion is either looping or somewhat of a sinusoidal motion (see video http://www.youtube.com/watch?v=3m8scBDIyWM"). However in reality I have yet to see a top behave in that way, they seem to have very steady precession (Euler's angle theta stays at zero). What is the reason for this?

2) Also, Wikipedia discusses three integrable cases for spinning tops (http://en.wikipedia.org/wiki/Lagrange,_Euler_and_Kovalevskaya_tops" !). I only understand Lagrange solutions, not Hamiltonian, so it's not making too much sense to me (someone point me to an online source on Hamiltonian for beginners!). Are these special cases real life applications or somewhat theoretical (as like in point 1, where I cannot find a spinning top behaving in that manner)

Thanks for the help people!
 
Last edited by a moderator:
Physics news on Phys.org
Bump :D

Does anyone know what the Kowalevsky top is about? I'm confused about it because there is no 'Kowalevsky toy' that can give me a visual representation of motion
 

Similar threads

Graduate The order of Euler Angle rotations for a top
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Two precession rates for a spinning top (forced precession)
  • · Replies 4 ·
Replies
4
Views
6K
Angular momentum direction for a spinning top
  • · Replies 10 ·
Replies
10
Views
4K
Graduate Why does the spinning book have an unstable axis?
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Precession - why does the rotational axis change as L changes?
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Can Any Quantifiable Variable Serve as a Coordinate in Euler-Lagrange Equations?
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Puzzling precession of the torque-free symmetric top
  • · Replies 13 ·
Replies
13
Views
6K
Graduate Spin parity and attractive/repulsive forces
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Atmospheric Density vs Altitude in an O'Neil Cylinder
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Prospects of spin foam formalism in loop quantum gravity [Alexandrov, Roche]
  • · Replies 9 ·
Replies
9
Views
6K