Langrangian Mechanics

  • #1
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Hi, I'm in the masters year of a theoretical physics course which begins this September. I'm reading the classical mechanics notes ahead of time, and I came across the idea of holonomic and non-holonomic constraints. I understand that in the case of a holonomic system, you can use the constraints to reduce the number of variables needed to describe that system, and thus find generalised co ordinates. I'm a bit unclear on what constitutes a holonomic constraint though. Any information I've found online seems to only tell me two things:

That a holonomic constraint can be represented in the form f(q, t) = 0, (With q being generalised co-ordinates) and
That a holonomic constraint is an equality, whereas a non-holonomic constraint is an inequality.

These seem a bit vague though, and any advice or tips would be very helpful!

Thanks!
 

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  • #2
andrewkirk
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That a holonomic constraint can be represented in the form f(q, t) = 0, (With q being generalised co-ordinates)
That is correct
That a holonomic constraint is an equality, whereas a non-holonomic constraint is an inequality.
That is not correct. A non-holonomic constraint is any constraint that is not holonomic. It may be an inequality. But non-holonomic constraints that crop up more often are those that involve generalised velocities ##\dot q_j##. A constraint of the form ##g(q,\dot q,t)## is non-holonomic, unless ##\frac{\partial g}{\partial \dot q}=0## (in which case the constraint can be written as ##h(q,t)=0## where ##g(q,\dot q,t)=h(q,t)##).
 

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