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[Jeremy McCreary]

Update on the Jellett "constant":  Toward the end of Reply #19, I mentioned this quantity as a possible constant of motion in high-CM ball-tipped tops. If so, precession rate should increase steadily as stem tilt increases and the CM descends during spin-down.

Then I listened more carefully to the sounds made by the high-CM LEGO test tops in the video I posted in Reply #13. Sure sounds like the precession rate decays during spin-down. Ditto when I retested the same tops afterward.

So today I tried to measure the precession rate with a high-speed strobe light. When that failed, I spun the tops on a dark surface and tried to time the passage of a light-colored ball tip through the beam of a laser tachometer. That worked a lot better, but the readings were still too inconsistent to report.

Nevertheless, the trend was pretty clear: Precession rate really does decay rather than increase during the CM's descent, though apparently much more slowly than the spin rate does. That could only mean that the Jellet "constant" isn't really constant in my test tops -- presumably because underlying assumptions aren't being met.

It may also mean that there's a lot more rolling than slipping -- at least during portions of my spin-downs. I don't know what assumptions I might have violated, but when it applies, the Jellett constant is supposedly constant for any amount of slip or lack thereof.

[ta0]

I have not read the literature about this "Jellet constant" but here is a guess: it's constant if you can neglect the energy loss due to friction (but if there is slippage there has to be some energy loss).

[Jeremy McCreary]

I have not read the literature about this "Jellet constant" but here is a guess: it's constant if you can neglect the energy loss due to friction (but if there is slippage there has to be some energy loss).

I agree, spin decay could easily be the broken assumption here, whether due to tip friction or aerodynamic drag.

Now that you mention it, the 2 articles I have that mention the Jellet constant treat the torques about the CM due to tip friction but ignore the effect on spin rate, which was probably assumed constant. Nor was drag considered in any way.

In fact, I've never seen a quantitative treatment of top behavior that made any attempt to take dissipative spin decay into account -- and not for lack of searching on my part. Not even numerical treatments. Worse yet, those admitting that they're ignoring spin decay due to tip friction seldom even mention drag, which is probably the greater braking torque in many if not most real tops at speed.

For that reason alone, we have to be careful about applying formulas and calculations to real tops. The only formulas that don't suffer directly from ignoring spin decay are the formulas for the minimum speeds for stable sleeping and steady precession. Unfortunately, other practical issues complicate their application to real tops.

[Russpin]

In fact, I've never seen a quantitative treatment of top behavior that made any attempt to take dissipative spin decay into account -- and not for lack of searching on my part. Not even numerical treatments.

I modeled spin decay in my spherical tip top simulation. This simulation is realistic up to the point where the the rim of the top touches the horizontal surface. The dynamics of two contact points is not modeled very well.
http://www.ta0.com/forum/index.php/topic,4637.0.html

[Jeremy McCreary]

In fact, I've never seen a quantitative treatment of top behavior that made any attempt to take dissipative spin decay into account -- and not for lack of searching on my part. Not even numerical treatments.

I modeled spin decay in my spherical tip top simulation. This simulation is realistic up to the point where the the rim of the top touches the horizontal surface. The dynamics of two contact points is not modeled very well.
http://www.ta0.com/forum/index.php/topic,4637.0.html

Indeed you did, and it's a spectacular simulation at that! I just got so distracted with the tip friction model you used that I missed the spin decay part. I have some questions about the simulation that I'll be posting in the original thread in the next day or so.

Here, however, I'd like to encourage you to consider publishing your simulation with spin decay. There really is a void in the literature here, and you could help to fill it. I can easily see such an article in the American or European Journal of Physics, both of which have published a string of top-related articles over the years.

[Russpin]

Here, however, I'd like to encourage you to consider publishing your simulation with spin decay.

Thanks Jeremy.
The two contact point dynamics model needs to be improved before I would consider publishing.
I emailed Dr. Moffatt asking if he had done any work on non-convex spinning objects and he said he had not.

[Larry D.]

That is great!

Those are beautiful the two large white ones seemed to be in a mating ritual.

I love it!  What a great video!!  I can't wait to watch it again!!!

It sure is! 

At 11:50-11:55 it reminds me of a fish out of water.

Nice movement. 

[ta0]

Here is a video of Philippe Dyon's high-center of mass top. I think it's one of the most amazing tops out there.

https://www.youtube.com/watch?v=VOjgktYgiv8

I recorded it at 120 and 240 fps but it was not enough to follow the spin during the flip (I recorded it outside to have plenty of light). I will need to go higher.
You can see a little of nutation when it is almost lying down. I nutates nicely when pushed down in that situation.

[the Earl of Whirl]

It is so elegant when it is spinning on the long stem.  When it slows it looks like it is just about to lay down, but that is when all the excitement starts.  Very unusual.  I remember watching Didier play with this kind of top.  I always loved his happy reaction!!!

Thanks for the slow motion.  I want to watch it several more times.

[ta0]

Ludo found this video of a top made with a golf ball, an ebony ball as a tip and a thin rod (looks dangerous).

https://www.youtube.com/watch?v=Agon77cdmdE

The description says it was started with a string and wooden fork that holds the rod. The top is 20 cm tall.

[Iacopo]

Nice find ! It reminds me the biconical tops and the spinning tubes, the dynamics seems to be the same.
Interesting to see the golf ball practically not to wobble until touching the ground.

My guess is that the slow wobble in the beginning is not precession but "hula hooping", which can happen when the tip of the top is ball shaped and the spinning surface is concave. The fast wobble about the golf ball should be the precession, (torque induced wobble).

[Jeremy McCreary]

Ludo found this video of a top made with a golf ball, an ebony ball as a tip and a thin rod (looks dangerous).

Excellent! I see this same spin-down behavior in LEGO tops with this mass distribution and ball tips of the right size. Also in the fun little Torendao (sp?) from Spin Gear.

I like to arrange for the main mass to end up at the top's final CM. The terminal horizontal spin then lasts a long time. If necessary, use small sliding accessory masses on the central axle to make this happen.