This paper describes a method for interactive manipulation of digital human models using the Lagrange multiplier method to simulate their motion under the approximation of first order dynamics, where F = mν. This method provides a natural framework for mixing rigid constraints with flexible goals in both Cartesian and joint space. Features like gravity and contact can thus be incorporated according to strict mathematical principles. We have implemented such a system for the specific task of positioning vehicle occupant models. Although the Lagrange multiplier method for solving constrained dynamics is well documented, its utility in this context has not been widely recognised.