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Colloquium, Winter 2005

Day: Thursday January 27 Time: 4:00pm Place: BH 106 Title: Generalized Variational Principle of Herglotz. Noether-type theorems Speaker: Bogdana Georgieva, Oregon State University Abstract: As is well known, a variational description of a system is very desirable both from mathematical and from physical points of view. Fairly recently, Gustav Herglotz formulated a variational principle which is more general than the classical variational principle and contains the classical variational principle as a special case. In the Herglotz variational principle the functional, whose extrema are sought, is defined by a differential equation instead of the classical variational integral. This variational principle is important for a number of reasons. Notably, it is closely related to contact transformations and it can give a variational description of nonconservative processes. It is also very suitable for use in control and optimal control problems. I will talk about some examples for applications to nonconservative processes in mechanics, to the nonlinear damped Klein-Gordon equation, and to the propagation of electromagnetic waves in conductive medium. (A variational description of these processes is not possible with the classical variational principle.) I will also talk about two new theorems which provide the conservation laws corresponding to finite and infinite-dimensional groups of transformations of the system described with the generalized variational principle. These theorems contain the first ans second Noether theorems as special cases. Cookies: In BH 300 at 3:30pm.