GEOMETRIC MECHANICS I
Math 580
Time and Place: 1-1:50 pm at Engineering E205
Instructor: Vakhtang Putkaradze, Department of Mathematics
Office hours: MWF 11-12 or by appointment.
Course Objectives:
At the end of this course the student will be able to set up and analyze geometric problems inspired by mechanics and optics. The emphasis of the course is to make students comfortable in solving geometric problems in the coordinate-free form as well as treating concrete problems. The students will also understand how to apply all these mathematical concepts to problems in mechanics and optics.
Syllabus (enumerated by weeks)
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1) Fermat's principle
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2) Hamiltonian formulation of ray optics
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3) Hamiltonian form of optical transmission
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4) Geometric picture in invariant coordinates
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5) Newton's laws
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6) Lagrange's principle
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7) Hamilton's equations
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8) Symplectic manifolds and differential forms
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9) Lie derivative and Poincare's theorem
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10) Resonances
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11) Dynamics phase
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12) Elastic spherical pendulum
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13) Mathematical analyses of other instructor-chosen problems in mechanics
Grading.
There will be 4 tri-weekly homeworks in the course. It is possible to replace last homework with an oral presentation by agreement with the professor. Each homework is 25% of the grade.
The text is Geometric Mechanics I, by D. D. Holm, Imperial College Press.
Class cancellations:
Feb. 13 (trip to ABQ)
Links to homeworks are given below.
Due Monday, Feb 16
Due Wednesday, March 25
Due Wednesday, May 6