In classical mechanics, particularly Lagrangian Mechanics, a holonomic constraint is a special type of constraint of motion. It restricts the trajectory of a system of particles to a smooth manifold Q by the set smooth equations

a({x},t)=0
b({x},t)=0
.
.
.
Where
t=time
{x}= the set of 3N Cartesian coordinates for the system of N particles.

For N particles, the number of holonomic constraints must be less than 3N using the assumption that each equation has an explicit dependence to AT LEAST one coordinate.

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