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The paper presents a simple, robust, and effective constraint enforcement scheme for rigid body dynamic simulation. The constraint enforcement scheme treats the constraint equations implicitly providing stability as well as accuracy in constrained dynamic problems. The method does not require ad-hoc problem dependent parameters. We describe the formulation of implicit constraint enforcement for both holonomic and non-holonomic cases in rigid body simulation. A first order version of the method is compared to a first order version of the well-known Baumgarte stabilization.

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This paper describes formulation and management of constraints, and a nonlinear optimization algorithm that together enable interactive geometrically aware manipulation of articulated objects. Going beyond purely kinematic or dynamic approaches, our solution method directly employs geometric constraints to ensure non‐interpenetration during object manipulation. We present the formulation of the inequality constraints used to ensure nonpenetration, describe how to manage the set of active inequality constraints as objects move, and show how these results are combined with a nonlinear optimization algorithm to achieve interactive geometrically aware object manipulation. Our optimization algorithm handles equality and inequality constraints and does not restrict object topology. It is an efficient iterative algorithm, quadratically convergent, with each iteration bounded by O(nnz(L)), where nnz(L) is the number of non‐zeros in L, a Cholesky factor of a sparse matrix.