The article presents a theoretical framework for molecular dynamics simulations of complex systems subject to any combination of holonomic and non-holonomic constraints. Using the concept of constrained inverse matrices both the particle accelerations and the associated constraint forces can be determined from given external forces and kinematical conditions. The formalism enables in particular the construction of explicit kinematical conditions which lead to the well-known Nosé–Hoover type equations of motion for the simulation of non-standard molecular dynamics ensembles. Illustrations are given for a few examples and an outline is presented for a numerical implementation of the method.