Degrees of freedom and constraints

[Ahmed1029]

In case of P holonomic constraints and N particles, I have 3N-P degrees of freedom and I have to look for 3N-P generalized coordinates if I want them to vary independently, but what about non-holonomic constraints? I know if I have N particles and P non-holonomic constraints, I still need 3N coordinates to completely describe the mechanical system, but do those 3N coordinates vary independently?(assume I'm talking about any set of coordinates, not just cartesian)

 

[andresB]

In systems with non-holonomic constraints, we always need more coordinates than degrees of freedom. Of course, those coordinates do not vary independently, they have to obey the non-holonomic constraint.

 

[strangerep]

FYI: the handling of non-holonomic constraints is still an active research area. Google for "Flannery nonholonomic" to see some relevant references.