Hamel's Formalism and its Applications

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This project develops a representation of Lagrangian mechanics in which the velocity components are measured relative to a frame that is not related to any local coordinates on the configuration space. This approach offers more flexibility than the original formalism of Lagrange, while keeping a clear distinction between system configurations and velocities. Known to be an effective and powerful tool in finite-dimensional continuous-time mechanics, this formalism introduced by Georg Hamel has not yet been fully developed for systems with infinitely-many degrees of freedom. The project is aimed at systematic study of the formalism in the infinite-dimensional setting, understanding its variational structure, its applications to dynamics of infinite-dimensional systems with nonholonomic constraints, including stability of a liquid-filled rigid body subject to nonholonomic constraints, and Lyapunov function construction.Systems with infinite number of degrees of freedom arise in many applications in engineering and industry. Examples include flexible structures and rigid bodies interacting with fluids. This project develops the mathematics required to model and simulate the behavior of such complex mechanical systems. This work on the mechanics of systems will further integrate mathematics and theoretical engineering. The results of the project will be useful in theoretical analysis, simulations, control, and study of the long time behavior of multi-body dynamics and complex mechanical systems.