This course covers the learning outcomes and goals of understanding Hamiltonian normal forms, Lie series method for finding canonical transformations, and infinite-dimensional Hamiltonian systems, particularly partial differential equations like the shallow water equations. The individual skills taught include simplifying Hamiltonian functions, applying the Lie transformation method, and analyzing infinite-dimensional systems. The teaching method involves lectures and examples to illustrate concepts. The intended audience for this course is graduate students or professionals interested in advanced dynamics, Hamiltonian systems, and nonlinear dynamics.
Hamiltonian Normal Forms, Lie Series Method for Transformations - Infinite-Dimensional Hamiltonians
Overview
Syllabus
Normal forms for general ODEs.
Hamiltonian normal forms.
Lie transformation method for finding a canonical transformation.
Simplifying the Hamiltonian function via the Lie series method.
Example 1 degree of freedom system to simplify via normal forms.
Infinite-dimensional Hamiltonian systems (PDEs).
Example: shallow water equations (Korteweg-de Vries or KdV equation).
Taught by
Ross Dynamics Lab
