What is the meaning of nonholonomy in a system?

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Discussion Overview

The discussion revolves around the concept of nonholonomy in mechanical systems, particularly in the context of spherical robots and their control. Participants seek to clarify the meaning of nonholonomic constraints and how they differ from holonomic constraints, as well as the implications for system behavior.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant expresses confusion about the term nonholonomy and its relevance to mechanical systems, specifically in relation to spherical robots.
  • Another participant explains that holonomic systems have constraints that can be expressed solely in terms of coordinates, while nonholonomic systems have constraints that depend on velocities, leading to more complex behavior.
  • A participant questions why a ball rolling on a plane is considered complex, seeking further understanding of nonholonomic constraints.
  • It is noted that non-holonomic constraints cannot be eliminated through coordinate transformations, which adds to the complexity of analyzing such systems.
  • References to Goldstein's textbook on classical mechanics are provided as a resource for deeper understanding of the topic.

Areas of Agreement / Disagreement

Participants generally agree on the definitions of holonomic and nonholonomic constraints, but there remains uncertainty regarding the implications of these constraints for system behavior, particularly in specific examples like the ball on a plane.

Contextual Notes

Participants express a need for more comprehensive resources beyond qualitative descriptions, indicating limitations in their current understanding and the complexity of the topic.

indianaronald
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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?
 
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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
 
Jano L. said:
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

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.
 
But why is a ball on a plane complex? I don't understand that all.
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.
 
Jano L. said:
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.

Thank you. That is exactly what I was looking for.
 
indianaronald said:
Thank you. That is exactly what I was looking for.

what is the book called?
 
Kidphysics said:
what is the book called?

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

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