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.

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.

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.

\left| {x_i - x_j } \right| - c_{ij} = 0

where i is not equal to j is a Holonomic Constraint.

by pinu7
November 11, 2009