Lecture

Non-linear dynamics: phenomenology, tools and methods

In course
DEMO: excepteur minim irure consequat
Nostrud nisi eiusmod anim cillum voluptate deserunt sunt. Aute nostrud mollit laboris minim excepteur commodo et officia consectetur dolor sit laborum reprehenderit elit. Adipisicing Lorem enim nisi sint magna aute eiusmod dolor. Ea dolor et dolor exercitation ad ea sint incididunt sint officia ullamco minim ad fugiat.
Login to see this section
Description

This lecture covers the variables in Hamiltonian and Lagrangian formulations, the concept of Phase Space and Configuration Space, Action-Angle variables, Hamilton and Hamiltonian principles, Lagrange function, canonical variables, Hamiltonian for electromagnetic fields, Lie operators, Poisson brackets, Lie transformations, and applications in beam dynamics. The instructor explains the significance of Lie transforms in describing nonlinear elements, symplecticity, and the generation of transfer maps. The lecture delves into the analysis of Hamiltonians for machine elements, the derivation of invariants, and the application of Lie transforms in beam-beam interactions. The discussion extends to the calculation of tunes, chromaticities, and the importance of normal forms in nonlinear systems.

Instructors (3)
nisi cupidatat occaecat
Excepteur consectetur eiusmod veniam et amet. Nostrud officia amet eu cupidatat dolor. Dolore velit exercitation consectetur consequat velit labore ea aliqua eu cillum laboris aliquip consectetur. Mollit voluptate ea proident veniam qui ex. Pariatur eu reprehenderit sit deserunt enim sint non est elit duis enim.
amet aliquip occaecat dolore
Pariatur aliqua minim ad culpa officia dolore commodo consequat. Lorem incididunt nisi culpa eiusmod exercitation exercitation nulla esse cillum reprehenderit id anim velit. Ut aliqua qui cillum in anim Lorem deserunt. Consequat aute et cupidatat et. Tempor consectetur exercitation ex anim duis nisi cupidatat.
sunt deserunt nisi veniam
Culpa dolor cupidatat do quis anim sint excepteur commodo sint dolor in ea culpa ipsum. Eiusmod ut nisi in reprehenderit pariatur et in ipsum do. Sint aute dolore voluptate do ad.
Login to see this section
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Ontological neighbourhood
Related lectures (33)
Hamiltonian Mechanics: Phase Space and Poisson Bracket
Explores phase space, the Poisson bracket, and Hamiltonian mechanics concepts.
Non-linear dynamics
Explores practical applications in nonlinear dynamics, emphasizing symplectic integration methods and thin lens approximations for accurate computations in accelerator physics.
Hamilton's Formalism: Equations and Transformations
Explores Hamilton's formalism, canonical equations, and Poisson brackets in classical and quantum mechanics.
Quantum Physics I
Explores discrete and continuous degrees of freedom, canonical commutation relations, and the correspondence between classical and quantum mechanics.
Functional Derivatives
Covers the concept of functional derivatives and their calculation process with examples.
Show more

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.