Computational Dynamics, 3rd Edition

Chapter 6. CONSTRAINED DYNAMICS

As shown in the preceding chapter, when the kinematic relationships are expressed in terms of the system degrees of freedom, the application of the principle of virtual work in dynamics leads to a number of dynamic differential equations equal to the number of the system degrees of freedom. In these equations the forces of the workless constraint are automatically eliminated. Constraint forces, however, appear in the dynamic equations if these equations are formulated in terms of a set of coordinates that are not totally independent, as discussed in Chapter 4. The number of independent constraint forces that appear in these equations is equal to the number of dependent coordinates used in the dynamic formulation.

In this chapter, the concepts and techniques, presented in Chapter 4 based on the Newtonian approach and D'Alembert's principle, are generalized using the technique of the virtual work presented in the preceding chapter. The principle of virtual work can be used to provide a proof for the existence of Lagrange multipliers when redundant coordinates are used with the augmented formulation. The virtual work principle, as demonstrated in the preceding chapter, can also be used to systematically define the velocity transformation required in the case of the embedding technique. In this chapter, the general augmented form of the equations of motion of multibody systems that consist of interconnected bodies is developed using the absolute Cartesian ...