Holonomic

In mathematics, the term holonomic may occur with several different meanings.

=Holonomic basis=

A holonomic basis for a manifold is a set of basis vectors e k for which all Lie derivatives vanish: :[e_j,e_k]=0

Some authors call a holonomic basis a coordinate basis, and an anholonomic basis a non-coordinate basis. See also Jet bundle.

=Holonomic system=

In Classical Mechanics a system may be defined as holonomic if all the constraints of the system are holonomic. For a constraint to be holonomic it must be expressible as a function (mathematics): f(x_1, x_2, x_3, ... x_n, t) = 0 .

Examples of holonomic systems are: the simple pendulum [√(x² + y²) L =0]; rigid bodies. See also nonholonomic system.