D.J. Braun and M. Goldfarb, Simulation of Constrained Mechanical Systems – Part I: An Equation of Motion, ASME Journal of Applied Mechanics, vol. 79, issue 4, 041017, 2012.
This paper introduces an equation of motion for simulating constrained mechanical systems with holonomic and nonholonomic constraints. The formulation embeds force and impulse terms that continuously correct for constraint violations and energy drift, avoiding error accumulation common in numerical simulations. By separating constraint enforcement and energy conservation within the dynamics, the method enables efficient explicit integration without the need for costly implicit solvers or iterative stabilization. Its effectiveness is demonstrated on a representative example, with further details provided in Part II.
Why it matters: Accurate and efficient simulation of constrained systems is essential for robotics and mechanical design. This work provides a robust numerical approach that improves stability and computational efficiency, supporting more reliable simulations for complex constrained dynamics.