Hamel's formalism is a representation of Lagrangian mechanics in which the velocity components are measured relative to a frame that is not related to any local configuration coordinates on the configuration space. This approach offers more flexibility than the original formalism of Lagrange while keeping a clear distinction between system's configurations and velocities. That distinction may be lost in Hamilton's formalism. The PI proposes further develop Hamel's formalism and extend it to systems with infinitely-many degrees of freedom. The PI then intends to use this formalism for studying the dynamics and stability of rigid bodies with liquid-filled cavities subject to velocity constraints. The PI also proposes to adopt Hamel's formalism for discrete mechanical systems.

Dr. Zenkov proposes to study the dynamics of discrete nonholonomic systems and applications of discrete mechanics to control problems. This includes the development of structurally stable integrators for nonholonomic systems and the use of discrete mechanics in problems of stabilization of periodic orbits.

The theory of nonholonomic dynamics is the study of mechanical systems subject to constraints imposed on velocities. Such constraints are typical for systems consisting of rigid bodies rolling on surfaces without slipping. Nonholonomic systems occur frequently in practical mechanical problems. Nonholonomic systems are closely linked to nonlinear control theory because of the key role played in control by noncommuting vector fields. The Principal Investigator proposes to study (i) the geometry and dynamics of constrained systems with symmetry and in particular the dynamics of infinite-dimensional nonholonomic systems; (ii) discrete nonholonomic systems and their structure-preserving properties; (iii) control by changing internal degrees of freedom; (iv) applications of variational integrators to control problems.