I Degrees of freedom and constraints

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In systems with P holonomic constraints and N particles, there are 3N-P degrees of freedom, requiring 3N-P generalized coordinates for independent variation. For non-holonomic constraints, despite needing 3N coordinates to fully describe the system, these coordinates do not vary independently due to the constraints imposed. Non-holonomic constraints necessitate more coordinates than degrees of freedom, as they must adhere to specific relationships. The handling of non-holonomic constraints remains an active area of research, with ongoing developments in the field. For further insights, references such as "Flannery nonholonomic" can provide additional information.
Ahmed1029
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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)
 
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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.
 
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FYI: the handling of non-holonomic constraints is still an active research area. Google for "Flannery nonholonomic" to see some relevant references.
 
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