Multi-multiplier ambient-space formulations of constrained dynamical systems, with an application to elastodynamics

Various formulations of the equations of motion for both finite- and infini te-dimensional constrained Lagrangian dynamical systems are studied. The di fferent formulations correspond to different ways of enforcing constraints through multiplier fields. All the formulations considered are posed on amb ient spaces whose members are unrestricted by the need to satisfy constrain t equations, but each formulation is shown to possess an invariant set on w hich the constraint equations and physical balance laws are satisfied. The stability properties of the invariant set within its ambient space are show n to be different in each case. We use the specific model problem of linear ized incompressible elastodynamics to compare properties of three different ambient-space formulations. We establish the well-posedness of one formula tion in the particular case of a homogeneous, isotropic body subject to spe cified tractions on its boundary.