What is the meaning of nonholonomy in a system?

indianaronald

I keep coming across this term and I cannot understand what this means pertaining to a mechanical system. I'm working on spherical robots and their control and there is mention of nonholonomy in the control of spherical robots. I googled it but I couldn't find a clear starting point to start reading. Someone point me to the fundamentals or something from where this starts?

Jano L.

If I remember correctly, it has to do with the kind of constraints the system has. If the constraints are functions of coordinates only, the system is holonomic. This usually means the system is "simple" to analyze (mass point on a circle).

If the constraints cannot be expressed via coordinates only, but are functions of velocity or even worse, the system is non-holonomic. Then we expect the system to behave in am more complex way. (ball rolling on plane surface without slipping).

https://en.wikipedia.org/wiki/Holonomic_constraints
https://en.wikipedia.org/wiki/Nonholonomic

indianaronald

yeah..but I need to understand this fully and properly. I read the wiki page and like all wiki pages it's qualitative at best. I was hoping for some book or topic which covers this extensively. But why is a ball on a plane complex? I don't understand that all.

Jano L.

Because non-holonomic constraint cannot be removed by coordinate transformation and elimination of the constraint variable. To see the details, try to get Goldstein's textbook, sec. 1.3 - he explains this nicely.

indianaronald

Thank you. That is exactly what I was looking for.

Kidphysics

what is the book called?

indianaronald

classical mechanics by Goldstein. Google it. It's available on scribd.