Can an ideal spinning top spin and precess forever?

[ehrenfest]

[SOLVED] spinning top

Homework Statement

Please confirm the following:
1) If a the tip of a top is perfectly sharp and everything else about the top is perfect and there is no air resistance, then you can put the top to sleep forever i.e. you can make it spin around the vertical axis forever.
2) With the same ideal conditions as in 1), you can make the top precess forever about the vertical.

Homework Equations

The Attempt at a Solution

 

[pam]

Both are correct. There is no mechanism for energy loss with no friction or air resistance.