In this report some aspects of the analytical and numerical solution of Partitioned Dynamical Systems (PDSs) are discussed. A PDS is solved using the Lagrange multiplier approach. The resulting equations are combined to obtain Differential-Algebraic Equations, describing a PDS. The additional algebraic equation leads to error accumulation when a numerical solution is sought. To avoid this, a correction term is applied. This correction term proved to be applicable with the Forward-Euler integration method and with the Runge-Kutta (Merson) integration method. Finally, this report discusses some topics that merit further attention, such as: different integration schemes, inequality constraints, and error accumulation.