Holonomic Constraint


in cl-ssical 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 -ssumption that each equation has an explicit dependence to at least one coordinate.
a rigid body, defined by the constraint equations (using latex) is

\left| {x_i – x_j } \right| – c_{ij} = 0
where i is not equal to j is a holonomic constraint.

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