Elimination Approach for Constraints on Rigid Body Systems

There are several ways to enforce constraints in rigid-body systems, which are commonly classified as elimination or augmentation methods. One example of augmentation is the use of Lagrange multipliers in Lagrangian dynamics, which often yields more equations than the minimum required to describe the system’s dynamics. Elimination methods typically yield a minimal set of equations equal to the system’s degrees of freedom. However, this process usually requires an explicit choice of independent and dependent coordinates, an operation often referred to as coordinate partitioning. This paper presents an alternative approach that avoids this choice. Instead, the method reformulates the state space so that constraints are embedded directly within the model. This reformulation can simplify the model and reduce the equations of motion to a minimal form. The approach was previously applied to the normalization constraint on Euler parameters; here, it is illustrated using the nonholonomic no-slip rolling constraint of a disk in three-dimensional motion.