Holonomy

In differential geometry, the holonomy of a connection on a smooth manifold is a general geometrical consequence of the curvature of the connection measuring the extent to which parallel transport around closed loops fails to preserve the geometrical data being transported.

Person 1: What‘s holonomy?
Person 2: In differential geometry, the holonomy of a connection on a smooth manifold is a general geometrical consequence of the curvature of the connection measuring the extent to which parallel transport around closed loops fails to preserve the geometrical data being transported.
Person 1: uhh

by Potato the Programmer October 22, 2023

Holonomic Constraint

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 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.

by pinu7 November 11, 2009