  This article describes an absolutely stable, first-order constraint solverfor
multi-rigid body systems that calculates (predicts) constraint forces for
typical bilateral and unilateral constraints, contact constraints with
friction, and many other constraint types. Redundant constraints do not pose
numerical problems or require regularization. Coulomb friction for contact is
modeled using a true friction cone, rather than a linearized approximation. The
computational expense of the solver is dependent upon the types of constraints
present in the input. The hardest (in a computational complexity sense) inputs
are reducible to solving convex optimization problems, i.e., polynomial time
solvable. The simplest inputs require only solving a linear system. The solver
is L-stable, which will imply that the forces due to constraints induce no
computational stiffness into the multi-body dynamics differential equations.
This approach is targeted to multibodies simulated with coarse accuracy,
subject to computational stiffness arising from constraints, and where the
number of constraint equations is not large compared to the number of multibody
position and velocity state variables. For such applications, the approach
should prove far faster than using other implicit integration approaches. I
assess the approach on some fundamental multibody dynamics problems.
