Speaker: Vakhtang PUTKARADZE (University of Alberta)
Date: March 23 Friday 16:30-18:00
Room: 55N-1F 1st Meeting Room, Nishi-Waseda Campus, Waseda University
Title: Variational approach to inertia, dissipation, and constraints realization.
We consider the problem of dissipative systems where the main part of dynamics can be described by Lagrangian methods. Such problems are frequently encountered in mechanical and electrical engineering problems. We shall focus mainly on the mechanical analogues of fluid-structure interaction, especially in the presence of friction. Variational approaches are particularly useful for deriving equations for arbitrary lagrangians. We discuss a variational approach to the dynamics of porous media by incorporating viscous forces in the variational principle. To elucidate the physics and mathematics of the problem, we study some simplified cases such as a pendulum with a moving viscous droplet. We show that the analog of Darcy's law for porous media (velocity proportional to force) in these simplified models comes from the short-term convergence to a ‘constraint manifold' in a singular perturbation problem and the following long-term dynamics on that manifold. The resulting Darcy's law can reduce to either holonomic or non-holonomic constraint for the motion, depending on the physical realization. We then discuss the relevance of our results to other dissipative systems and outline methods that can be useful for other applications in Mechanical and Electrical Engineering. This work was partially supported by NSERC and the University of Alberta.