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Pfaffian Constraints: Constraints on a system can be expressed as w(q)q_dot = 0, which is a set of k independent equations representing k constraints on the system. Each row w(q)_i constrains the direction in which q_dot is allowed to take non-negative values.

Holonomic Constraints: A set of constraints are called holonomic if they restrict the motion of the system to a smooth manifold. Locally, a holonomic constraint can be expressed as a set of k algebraic constraints on the configuration space: h(q) = 0; the dimension of the manifold is then n - k.

A set of k Pfaffian constraints are called integrable if it can be integrated to remove the dependency on q_dot. It is then equivalent to a set k holonomic constraints