In this paper, the following problem is analyzed: Given a frictionless Lagrangian system subject to complementarity relations (due to a set of unilateral constraints) that define a linear complementarity problem whose matrix is the so-called Delassus' matrix, study the influence of a set of bilateral constraints added to the dynamics on the Delassus' matrix. Two main paths are followed: the Lagrange multipliers method and the reduced coordinates method. The link with optimization (the Gauss' principle of mechanics) and the case of impacts, are also examined. The kinetic angles between the bilateral and the unilateral constraints are used to study the definiteness of the Delassus' matrix.