Holonomic system

In classical mechanics, holonomic constraints are relations between the position variables (and possibly time) which can be expressed in the following form: ${\displaystyle f(q_{1},q_{2},q_{3},\ldots ,q_{n},t)=0}$, where ${\displaystyle \{q_{1},q_{2},q_{3},\ldots ,q_{n}\}}$ are the n coordinates which describe the system. For example, the motion of a particle constrained to lie on the surface of a sphere is subject to a holonomic constraint, but if the particle is able to fall off the sphere under the influence of gravity, the constraint becomes non-holonomic.

Velocity-dependent constraints such as ${\displaystyle f(q_{1},q_{2},...,q_{n},{\dot {q}}_{1},{\dot {q}}_{2},...,{\dot {q}}_{n},t)=0}$ are not usually holonomic.

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