Understanding Holonomic Constraints in Lagrangian Mechanics

[FraserAC]

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!

 

[andrewkirk]

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 $g(q,\dot q,t)=h(q,t)$).