Why Do Spinning Tops Behave Differently in Theory and Reality?

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In summary, the conversation is about spinning tops and the Lagrange solutions for these tops. The speaker is trying to solve the equations of motion for these tops under gravity and has noticed that the resulting motion is either looping or sinusoidal, while real-life tops seem to have a steady precession. They ask for the reason behind this and also discuss the three integrable cases for spinning tops mentioned on Wikipedia, but they only understand the Lagrange solutions and are looking for resources on Hamiltonian for beginners. They also mention the Kowalevsky top and express confusion about it.
  • #1
James_Frogan
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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!
 
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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
 

1. What is the physics behind the behavior of spinning tops?

The behavior of spinning tops is governed by the principles of angular momentum, torque, and precession. When a top is spun, its angular momentum causes it to resist changes in its direction and orientation, while the torque applied by gravity or other forces causes it to precess, or wobble, around a vertical axis. This combination of angular momentum and torque results in the characteristic spinning motion of tops.

2. Why do tops spin for a longer time when they are spun with more force?

This is due to the conservation of angular momentum. When a top is spun with more force, it gains more angular momentum, which makes it more resistant to changes in its motion. This allows the top to spin for a longer time before coming to a stop.

3. How does the shape of a top affect its behavior?

The shape of a top can impact its behavior in several ways. A top with a wider base will have a lower center of mass, making it more stable and less likely to tip over. A top with a pointed tip will have less air resistance, allowing it to spin for a longer time. Additionally, the distribution of mass in a top can affect its precession and stability.

4. Can tops spin indefinitely?

In theory, yes, as long as there are no external forces acting on the top to slow it down. However, in reality, tops will eventually stop due to friction and air resistance. Additionally, imperfections in the top's shape or surface can also cause it to lose momentum and stop spinning.

5. How can we make tops spin for a longer time?

To make tops spin for a longer time, we can minimize external forces that can slow them down, such as reducing friction and air resistance. This can be achieved by using a smooth, flat surface and spinning the top in a vacuum. Additionally, using tops with pointed tips and distributing the mass evenly can also help to prolong their spin time.

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