Constrained Lagrangian and Hamiltonian Mechanics in Fluid-Body Interactions: Analytical Modeling and Computational Methods

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This project advances a novel perspective on the theoretical and computational modeling of interactions among solid bodies and vortical fluids, illuminating the fundamental presence of integrable and nonintegrable constraints in Lagrangian and Hamiltonian descriptions of such interactions. The project focuses on four distinct topics: (1) the formal equivalence of gyroscopic lift forces to nonholonomic forces of constraint, (2) the mathematical treatment of conditions of flow attachment or stagnation as holonomic or nonholonomic constraints, (3) the resolution of the Hamiltonian structure underpinning interactions of free bodies with discrete vortex distributions into constrained and unconstrained components, and (4) the realization of variational integration methods which preserve balance principles between vortex shedding from solid surfaces and the corresponding development of surface forces.Problems involving the dynamic interaction of fluids with solid structures abound in the natural and engineered worlds. A deeper understanding of such interactions promises to improve the design of systems ranging from robotic vehicles to energy-harvesting devices, but the subtle physics underpinning such interactions presents challenges to traditional mathematical modeling methods. This project will explore fundamental parallels between the modeling of fluid-structure interactions and the modeling of other mechanical phenomena, with the goal of illuminating pervasive physical principles and novel analytical techniques.