The topic of this thesis is the numerics of rigid body simulation, with focus on the contact force problem. Three contact force models are presented, followed by three contact point determination methods. To solve the contact force problem, six different numerical methods are presented, each tailored to solve problems in the form of one of the three contact force models.

The scientific contributions of this thesis, lies in part in the dissection of existing methods in which issues are uncovered and – where possible – fixes are suggested, and in part in the development of novel methods. A contact point determination method, based on boolean surface maps, is developed to handle collisions between tetrahedral meshes. The novel nonsmooth nonlinear conjugate gradient (NNCG) method is presented. The NNCG method is comparable in terms of accuracy to the state-of-the-art method, projected Gauss-Seidel (PGS), although computationally more expensive. The NNCG method has been implemented in the physics library Bullet, as of revision r2709, as an alternative to the PGS method. A subspace minimization method is developed to improve convergence of the PGS method, improving the results of large mass ratio simulations.