Abstract: In this talk, we present an extension of the Hamiltonian formalism for classical and continuum mechanics, introduced by Yochiro Nambu in 1973. We begin with a brief recap of the historical origin of Hamiltonian mechanics, as well as their mathematical formulation. Then, we proceed to sketch how this approach generalizes to continuum mechanics, how the Euler equations of fluid mechanics can be brought into Hamiltonian form and why the result leaves much to be desired. In the second half of the talk, we introduce Nambu mechanics and the Nambu bracket as a natural generalization of the Poisson bracket, initially in the realm of classical mechanics; we conclude with a discussion of the Nambu formulation of certain fluid dynamical systems and its connection to vorticity-like quantities, such as enstrophy and helicity.
Theoretical foundations of fluid dynamics: Nambu mechanics
08.02.2023 14:00 - 15:00
Organiser:
N. Mauser
Location: