Applied Math Seminar: The Intrinsic Linearization of Equilibria of Nonholonomic Systems

Speaker: Dr. George Patrick (U of S Math & Stats)

Date / Time: Tuesday, February 13th, 4:30 - 5:30

Room: ARTS 106

Title: The Intrinsic Linearization of Equilibria of Nonholonomic Systems

Abstract: Linearization about an equilibrium is one of the most important methods to approximate or analyze a nonlinear system. For Hamiltonian systems such linearizations are themselves Hamiltonian, with consequence that their spectrum is invariant under negation. By consequence, structurally either a Hamiltonian system departs an equilibrium or delicately oscillates about it with purely imaginary spectrum; asymptotic stability is precluded.

These structural restrictions do not persist to nonholonomic systems, such as are used to model rigid no-slip rolling. Yet, by following the underlying semi-symplectic geometry of nonholonomic systems to the linearized level (this geometry is universal for nonholonomic systems), one can derive the structure of the linearizations of their equilibria, and show for example that the linearization of the *ground state* of any nonholonomic system is fact naturally Hamiltonian.

(*This is not a colloquium and so there are no graduate student attendance requirements. However, interested grad students are encouraged to attend.)

Facebook Event: https://www.facebook.com/events/1623091024424206/