A Projection Method Approach to Constrained Dynamic Analysis

Abstract

The paper presents a unified approach to the dynamic analysis of mechanical systems subject to (ideal) holonomic and/or nonholonomic constraints. The approach is based on the projection of the initial (constraint reaction-containing) dynamical equations into the orthogonal and tangent subspaces; the orthogonal subspace which is spanned by the constraint vectors, and the tangent subspace which complements the orthogonal subspace in the system’s configuration space. The tangential projection gives the reaction-free (or purely kinetic) equations of motion, whereas the orthogonal projection determines the constraint reactions. Simplifications due to the use of independent variables are indicated, and examples illustrating the concepts are included.