Venue: A 212 (STCS seminar room)
Date and Time: Thursday, March 3, 2:00 pm
Abstract: This will be a one hour crash course on some of the basic ideas of classical mechanics: configuration space, Lagrangians, the principle of stationary action, and Noether's theorem. A reference is the online book http://math.ucr.edu/home/baez/classical/texfiles/2005/book/classical.pdf . In the discussion after the talk, we will work out some JEE physics-style mechanics problems. You are also invited to bring your own favorite mechanics problems.
The importance of classical mechanics is hard to exaggerate. It forms the basis of all of modern physics, and has inspired many deep ideas in mathematics, from manifolds and topology, to Lie groups and representation theory, to symplectic and Kahler geometry. Classical mechanics is also of obvious importance for understanding most physical phenomena, including most biological phenomena. This talk will not develop any of these connections.
Prerequisites: High school-level mathematics and physics, including integration by parts, should suffice.
Date and Time: Thursday, March 3, 2:00 pm
Abstract: This will be a one hour crash course on some of the basic ideas of classical mechanics: configuration space, Lagrangians, the principle of stationary action, and Noether's theorem. A reference is the online book http://math.ucr.edu/home/baez/classical/texfiles/2005/book/classical.pdf . In the discussion after the talk, we will work out some JEE physics-style mechanics problems. You are also invited to bring your own favorite mechanics problems.
The importance of classical mechanics is hard to exaggerate. It forms the basis of all of modern physics, and has inspired many deep ideas in mathematics, from manifolds and topology, to Lie groups and representation theory, to symplectic and Kahler geometry. Classical mechanics is also of obvious importance for understanding most physical phenomena, including most biological phenomena. This talk will not develop any of these connections.
Prerequisites: High school-level mathematics and physics, including integration by parts, should suffice.
I found this wonderful lecture on youtube by Professor Jerrold Marsden: http://www.youtube.com/watch?v=RLEeS1R3anU
ReplyDeleteNokia Distinguished Lecture: Jerrold Marsden on Discrete Mechanics and Optimal Control
Engineering and Control & Dynamical Systems
California Institute of Technology
Abstract:
We and Nature try to optimize things all the time; find the shortest route to the grocery store, find the most efficient way to throw a discus, cats turning themselves over efficiently, etc. Optimal control is about finding control forces to perform optimal ways of carrying out a task. Many such systems are mechanical and special techniques for computing optimal controls in mechanics will be presented. These techniques are based on recent progress in discrete mechanics. The techniques will be illustrated by systems such as falling cats, reorienting a network of satellites, optimal space mission design, systems with constraints (such as a satellite with momentum wheels), helicopter dynamics, and efficient 2D and 3D robotic walkers.
Bio:
Jerrold Marsden is a professor of Control and Dynamical Systems at Caltech. He has done extensive research in the area of geometric mechanics, with applications to rigid body systems, fluid mechanics, elasticity theory, plasma physics, as well as to general field theory. His work in dynamical systems and control theory emphasizes how it relates to mechanical systems and systems with symmetry. He is one of the original founders in the early 1970's of reduction theory for mechanical systems with symmetry, which remains an active and much studied area of research today. He has won a number of awards for his research.