Nonholonomic system

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In physics and mathematics, a nonholonomic system is a system in which a return to the original internal configuration does not guarantee return to the original system position. In other words, unlike with a holonomic system, the outcome of a nonholonomic system is path -dependent, and the number of generalized coordinates required to represent a system completely is more than its control degrees of freedom(sometimes called differential degrees of freedom, DDOF). In addition to the motion variables corresponding to the control degrees of freedom,the history of its motion too should be known.

For example, in the case of a vertical wheel which can spin as well as rotate about a vertical axis passing through its centre, the knowledge of these two variables (control variables) need not give a knowledge about its precise position from an inertial frame of reference. Similarly,when riding a two-wheeled cart, a return to the original internal (wheel) configuration does not guarantee return to the original system (cart) position.

Nonholonomic systems exist in at least three cases; Rolling, systems with inequality constraints and systems with constraints on velocity.

Cars, bicycles and unicycles are all examples of nonholonomic systems.

The branch of mathematics dealing with nonholonomic systems is known as sub-Riemannian geometry.Template:Classicalmechanics-stub