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Course Description

LecturerPaolo Muratore-Ginanneschi 
Credits10 (grading info)
LanguageEnglish
Master's Programme MAST/ Theoretical and Computational Methods
Time span15.01.2019 - 03.05.2019
VenueExactum Building
Lecture timetable
  • Tuesdays 10:15 - 12:00, Exactum, C321
  • Fridays 10:15-12:00, Exactum, BK106

QuestionnairePlease fill the form linked here
Exercise sessionWednesdays 10:15 - 12:00, Exactum, B321


The course is directed at physics and math-physics oriented  
students  at advanced undergraduate or graduate level. 

  • Elementary Newtonian Mechanics

  • Variational Lagrangian and Hamiltonian principles
  • Pontryagin's maximum principles
  • Noether's theorems and symmetries
  • Stability and Chaos

Requirements

The course requires linear algebra and differential calculus as discussed in the basic courses. 

Literature

The following textbook contains all material (and much more) which will be discussed in the course:

  1. Scheck, F. Mechanics: From Newton's Laws to Deterministic Chaos Springer-Verlag Berlin Heidelberg, 2010, XVI, 547. (Helka link)

Other useful references are

  1. Fasano, A. & Marmi, S. Analytical mechanics : an introduction Oxford Graduate Texts, 2006, XIII, 772. (Helka link)
  2. Cencini, M.; Cecconi, F. & Vulpiani, A. Chaos: From Simple Models to Complex Systems World Scientific, 2009 , 17, 460. (Helka link)
  3. Dumas, H. S. The KAM Story. A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov-Arnold-Moser Theory World Scientific Publishing, 2014, 380. (Helka link)

  4. Holm, D. D., Schmah, T. & Stoica, C. Geometric Mechanics and Symmetry: From Finite to Infinite Dimensions Oxford University Press, 2009 , 12, XVI, 536. (Helka link)

Finally a classical reference is

Arnol'd, V. I. Mathematical methods of classical mechanics Springer, 1989 , 60, 508.

Detailed Schedule


DayTimePlaceTopic
Tue 15.1.201910:15 - 12:00Exactum, C321, Pietari Kalmin katu 5Newton's laws
Fri 18.1.201910:15 - 12:00Exactum, BK106, Pietari Kalmin katu 5Existence and uniqueness theorems for ODEs (22.01)
Tue 22.1.201910:15 - 12:00Exactum, C321,  Pietari Kalmin katu 5Elementary properties of symplectomorphisms
Fri 25.1.201910:15 - 12:00Exactum, BK106,  Pietari Kalmin katu 5Linear systems
Tue 29.1.201910:15 - 12:00Exactum, C321,  Pietari Kalmin katu 5Linear Hamiltonian systems (25.03)
Fri 1.2.201910:15 - 12:00Exactum, BK106,  Pietari Kalmin katu 5Linear non-autonomous systems
Tue 5.2.201910:15 - 12:00Exactum, C321,  Pietari Kalmin katu 5Stability of periodic orbits
Fri 8.2.201910:15 - 12:00Exactum, BK106,  Pietari Kalmin katu 5Periodic orbits of Hamiltonian flows
Tue 12.2.201910:15 - 12:00Exactum, C321,  Pietari Kalmin katu 5Lyapunov exponents
Fri 15.2.201910:15 - 12:00Exactum, BK106,  Pietari Kalmin katu 5Mather's decomposition and local stretching exponents
Tue 19.2.201910:15 - 12:00Exactum, C321,  Pietari Kalmin katu 5A foray into the foundations of statistical mechanics
Fri 22.2.201910:15 - 12:00Exactum, BK106,  Pietari Kalmin katu 5Melnikov's method 
Tue 26.2.201910:15 - 12:00Exactum, C321,  Pietari Kalmin katu 5 Chain of harmonic oscillators
Fri 1.3.201910:15 - 12:00Exactum, BK106,  Pietari Kalmin katu 5Fermi-Pasta-Ulam-Tsingou model
Fri 15.3.201910:15 - 12:00Exactum, BK106,  Pietari Kalmin katu 5
Tue 19.3.201910:15 - 12:00Exactum, C321,  Pietari Kalmin katu 5Hamiltonian variational principle
Fri 22.3.201910:15 - 12:00Exactum, BK106,  Pietari Kalmin katu 5Pontryagin's principle
Fri 29.3.201910:15 - 12:00Exactum, BK106,  Pietari Kalmin katu 5Noether's theorems (02.04)
Tue 2.4.201910:15 - 12:00Exactum, C321,  Pietari Kalmin katu 5Noether's theorems (continued)
Wed 3.4.201910:15 - 12:00Exactum, B321,  Pietari Kalmin katu 5Equivariance and Poisson brackets (07.04)
Fri 5.4.201910:15 - 12:00Exactum, BK106,  Pietari Kalmin katu 5Canonical transformations
Tue 9.4.201910:15 - 12:00Exactum, C321,  Pietari Kalmin katu 5Hamilton-Jacobi equations
Fri 12.4.201910:15 - 12:00Exactum, BK106,  Pietari Kalmin katu 5Liouville Arnol'd integrability
Tue 16.4.201910:15 - 12:00Exactum, C321,  Pietari Kalmin katu 5Birkhoff normal forms
Fri 26.4.201910:15 - 12:00Exactum, BK106,  Pietari Kalmin katu 5Kolmogorov-Arnol'd-Moser theorem
Tue 30.4.201910:15 - 12:00Exactum, C321,  Pietari Kalmin katu 5Nekhoroshev's theorem
Fri 3.5.201910:15 - 12:00Exactum, BK106,  Pietari Kalmin katu 5

Exercises

Supplementary materialTime reversal
Exercise Session 01
Exercise Session 02
Exercise Session 03
Exercise Session 04
Supplementary materialGeneralized Lyapunov exponents
Exercise Session 05
Exercise Session 06
Supplementary materialSymplectomorphisms and first Noether's theorem
Exercise Session 07


Exercise Session 08


Exercise Session 09


Exercise Session 10


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