Based on Lagrangian mechanics, we present a novel and computationally efficient set of equations of motion in the matrix notation, for unconstrained or constrained mechanical systems including ignorable coordinates. The equations are applicable to multibody systems including holonomic or nonholonomic constraints. It is shown that by appropriate selection of generalized speeds as a new set of motion variables, the constraint reaction forces can be automatically eliminated from the set of developed reduced dynamical equations in a straightforward manner, resulting in a minimal set of dynamic equations. We present simulation results on one constrained and one unconstrained system to demonstrate the advantages of the proposed dynamic modeling approach for these different classes of dynamical systems. According to the results, the proposed dynamic equations not only reduce the number of equations and computational effort, but also better satisfy the invariance of constraints and conserved quantities of systems in comparison to the other conventional methods. © 2018 Elsevier Inc.