Holonomic constraints

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In a system of point particles, holonomic constraints can be expressed in the following form: $f(q_1, q_2, q_3,\ldots, q_{n}, t) = 0$ , where $\{ q_1, q_2, q_3, \ldots, q_{n} \}$ , are the coordinates of the $n$ particles. Holonomic constraints are rigid. For example, the motion of a particle constrained to lie on the surface of a sphere is subject to a holonomic constraint, but if the particle is able to fall off the sphere under the influence of gravity, the constraint becomes non-holonomic.

[edit] Use in Molecular Dynamics Simulations

Holonomic constraints are used in classical molecular dynamics simulations of molecules to restrict the motions of hydrogens attached to heavy atoms. These simulations use numerical methods to integrate the equations of motion of the molecular system. The stability of the numerical methods used determines how small the timestep of the integration must be in order to provide an accurate result. The fastest vibrating oscillators have the greatest effect on the timestep, but since these oscillators usually only represent bonds between hydrogen and heavier atoms, they are of little chemical interest. Imposing a holonomic constraint on heavy atom-hydrogen bonds makes the integration methods much more stable, at the relatively small cost of discarding uninteresting motions.^[1]