Discrete Constrained Lagrangian Systems and Geometric Constraint Stabilization

Abstract

We develop discrete Lagrangian systems with holonomic constraints by employing the discrete Lagrange‐d’Alembert principle, which was originally proposed by [5, 6]. Especially, we focus on the class of discrete holonomic Lagrangian systems in the context of the index 2 model, i.e., discrete Lagrange‐d’Alembert equations with velocity‐level constraints, while the lower index formulation may induce constraint violations called drift‐off phenomena. So we incorporate geometric constraint stabilization proposed by [7, 8] into the discrete holonomic Lagrangian systems in order to avoid the constraint violations. We demonstrate numerical validity in making use of discrete Lagrange‐d’Alembert equations for the index 2 model of holonomic mechanical systems with an illustrative example of linkage mechanisms.