Holonomic constraints
In classical mechanics, holonomic constraints are relations between the position variables (and possibly time) that can be expressed in the following form: f ( u 1 , u 2 , u 3 , … , u n , t ) = 0 {\displaystyle f(u_{1},u_{2},u_{3},\ldots ,u_{n},t)=0} where { u 1 , u 2 , u 3 , … , u n } {\displaystyle \{u_{1},u_{2},u_{3},\ldots ,u_{n}\}} are n generalized coordinates that describe the system (in unconstrained configuration space) and f {\displaystyle f} is a continuous function. 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.