Wednesday, April 16, 2014 at 3:00 PM in SAS 4201
Matthias Eller, Georgetown University
The shape derivative of boundary value problems
In the context of shape optimization the shape derivative is of fundamental importance. If the region in space or space-time underlying the boundary value problem (BVP) is allowed to vary in direction of a given vector field, one can compute the derivative of the solution to the BVP in direction of this vector field. The shape derivative for a wide class of BVPs for linear partial differential equations can be characterized as a solution of another BVP with a non-traditional boundary condition. Scalar equations and systems of equations will be considered and issues of regularity will be discussed.
Monday, April 21, 2014 at 3:00 PM in SAS 4201
Olga Rossi, University of Ostrava
Recent results in nonholonomic mechanics
In presence of constraints depending on velocities (i.e. given by a system of first order ODEs) one can investigate Lagrangian systems either from a mechanical or a geometrical point of view.The former approach reflects the physical understanding of constrained dynamics as motions in the original configuration space subject to reactive forces expressing the constraints.Mathematically this leads to equations of motion with Lagrange multipliers, known as Chetaev equations. We adopt the latter viewpoint reflecting a geometrical understanding of constrained dynamics as a motion on a submanifold of the first jet bundle, the so-called constraint manifold. This model leads to a reduced system of equations where the unknown reaction forces are absent (equationswithout Lagrange multipliers, equivalent with Chetaev equations). Remarkably, the geometric approach provides a unified treatment of both Lagrangian and non-Lagrangian systems subject to general (nonlinear non-ingerable) velocity dependent constraints. In particular, I shall present a solution of a longstanding problem about the existence of a variational principle for nonholonomic systems, and a corresponding Noether theorem.
Wednesday, May 7, 2014 at 3:00 PM in SAS 4201
Vakhtang Putkaradze, University of Alberta
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