kiwiheretic

Is that holonomic (seeing that the bead can swing above the cone but can't go through the cone)?

Isn't the friction along the surface so as to oppose the motion of the bead along it?

The rest of it made sense but what's interesting is Caikin never explained D'Alembert in this way (or at least not clearly). Anyway, I've decided to leave aside Caikin for now and pursue the topic through other texts.

studiot

Yes I believe it is holonomic. Well spotted.
But can the particle swing right over under rotation?
The upward forces can certainly be enough to lift it off the cone, but what happens then?

Yes the friction would oppose the motion of the particle relative to the cone, if it made any. But we stated the no slip condition.

I don't know Caikin so I can't comment.

A good book is Classical Mechanics by Gregory - Cambridge University press.

kiwiheretic

Then the centrifugal force = the tension force T ?

Pmb

Yes. Are you familiar with the difference between centrifugal force and centripetal force? For those who aren't please see the difference at:

https://en.wikipedia.org/wiki/Centripetal_force

https://en.wikipedia.org/wiki/Centrifugal_force

Pmb

Whether a system is holonomic or not depends on what is allowed for the constraint. For example: if a particle has the constraint of moving on a surface then it's a holonomic constraint. If the constraint is something like moving off a surface as well as on the surface then the constraint non-holonomic.

There are many PDF files on the web for examples of non-holonomic constraints/systems.