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Introduction to Hamiltonian Dynamics, Spring 2017

 

Teacher: Paolo Muratore-Ginanneschi

Scope: 7 cr

Type: Advanced

Teaching:

Topics: Classical Mechanics, Lagrange and Hamiltonian formalism, Chaos in Nonlinear Hamiltonian Dynamics.

Prerequisites:

News

Teaching schedule

16.1.-14.5.2017, Tue from 10-12, room C122. Exercise group Thu 10-12, room C122.

Exams

Exam lasts 2,5 hours.

You can use (lecturer will fill in) in the exam.

Course material

The course will draw mostly from the following references.

Course contents

Lecture 01: Examples of elementary dynamical systems 

Lecture 09: Lagrangean variational principles (14.03)
Lecture 02: Existence and uniqueness theorems for ODE’s  (01.02)Lecture 10: Hamiltonian variational principle
Lecture 03: Hamiltonian vector fields and time reversal  (08.02)Lecture 11: Noether's first and second theorem
Lecture 04: Linear systems, Hartman-Grobman theorem (08.02)Lecture 12: Equivariance and Poisson brackets
Lecture 05: Linear autonomous Hamiltonian systems (11.02)Lecture 13: Canonical transformations
Lecture 06: Linear periodic systems and stability of periodic orbitsLecture 14: Hamilton--Jacobi and dynamic programming
Lecture 07: Poincaré section, periodic orbits and Poincaré recurrence (02.03)Lecture 15: Liouville Arnold integrable systems
Lecture 08: D'Alembert principle and Euler–Lagrange equations (04.03)Lecture 16: Birkhoff integrable systems

 Lecture notes available from the latest installment of this course.

Registration



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Exercises

Assignments

  • Exercise set 1 (09.02)
  • Exercise set 2 (14.02)
  • Exercise set 3 (27.02)
  • Exercise set 4 (01.03)
  • Exercise set 5 (14.03)
  • Exercise set 6 (29.03: one typo corrected in assignment 1)
  • Exercise set 7
  • Exercise set 8
  • Exercise set 9

Exercise classes

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Course feedback

Course feedback can be given at any point during the course. Click here.

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