 For instance, in atomistic molecular dynamics, typically the length of covalent bonds to hydrogen are constrained; however, constraint algorithms should not be used if vibrations along these degrees of freedom are important for the phenomenon being studied.The motion of a set of "N" particles can be described by a set of second-order ordinary differential equations, Newton's second law, which can be written in matrix form

where M is a "mass matrix" and q is the vector of generalized coordinates that describe the particles' positions.For example, the vector q may be a "3N" Cartesian coordinates of the particle positions r"k", where "k" runs from 1 to "N"; in the absence of constraints, M would be the "3N"x"3N" diagonal square matrix of the particle masses.