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This article describes an absolutely stable, first-order constraint solverformulti-rigid body systems that calculates (predicts) constraint forces fortypical bilateral and unilateral constraints, contact constraints withfriction, and many other constraint types. Redundant constraints do not posenumerical problems or require regularization. Coulomb friction for contact ismodeled using a true friction cone, rather than a linearized approximation. Thecomputational expense of the solver is dependent upon the types of constraintspresent in the input. The hardest (in a computational complexity sense) inputsare reducible to solving convex optimization problems, i.e., polynomial timesolvable. The simplest inputs require only solving a linear system. The solveris L-stable, which will imply that the forces due to constraints induce nocomputational 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 thenumber of constraint equations is not large compared to the number of multibodyposition and velocity state variables. For such applications, the approachshould prove far faster than using other implicit integration approaches. Iassess the approach on some fundamental multibody dynamics problems.

An Unconditionally Stable First-Order Constraint Solver for Multibody Systems