Hamiltonian Mechanics
| Title | ΧΑΜΙΛΤΟΝΙΑΝΗ ΜΗΧΑΝΙΚΗ / Hamiltonian Mechanics |
| Code | ΓΘΕ202 |
| Faculty | Sciences |
| School | Physics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Winter |
| Coordinator | Efthymia Meletlidou |
| Common | No |
| Status | Active |
| Course ID | 40003062 |
Programme of Study: PROGRAMMA SPOUDŌN 2022
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| KORMOS | Basic Election | 7 | 4 | 7 |
| Academic Year | 2026 – 2027 |
| Class Period | Winter |
| Faculty Instructors |
|
| Weekly Hours | 4 |
| Class ID | 600307063
|
Course Type 2021
Specific Foundation
Course Type 2016-2020
- Scientific Area
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600307063
- At the Website of the School:
- eLearning: https://elearning.auth.gr/course/view.php?id=6165
Language of Instruction
- Greek (Instruction, Examination)
Prerequisites
General Prerequisites
Vector calculus, linear algebra and differential and integral calculus of one and many variables.
Learning Outcomes
With the conclusion of this course, the students will be able to:
-apply and analyse problem in mechanics.
-use some theories of physics (e.g., the principle of least action e.t.c.).
-to know the theory of Hamilton and its application to modern physics.
General Competences
- Apply knowledge in practice
- Work autonomously
- Advance free, creative and causative thinking
Course Content (Syllabus)
Definition of Hamiltonian Mechanics.
Hamilton’s equation, symplectic formalism, Poisson’s theorem.
Canonical transformations.Ggenerating function.
Symplectic matrices.
Infinitesimal canonical transformations (Hamiltonian vector field, infinitesimal symmetries and integrals of motion).
Stability of equilibrium points Liouville’s theorem, Poincare’s theorem.
The method of Hamilton-Jacobi, Integrable systems.
Liouville integrability and the theorem of Arnold-Liouville.
Action-angle variables.
Canonical theory of perturbation, small divisors, K.A.M. theorem. Poincare map.
Perturbed stadard map.Poincare-Birkhoff theorem.
Chaotic motion in Hamiltonian systems.
Keywords
Hamiltonian systems, Generating functions, Symplectic geometry, Infinitesimal canonical transformation, K.A.M. theorem Chaos in Hamiltonian systems
Educational Material Types
- Multimedia
- Book
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Course Teaching
- Use of ICT in Communication with Students
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 156 | 5.2 | |||
| Reading Assigment | 26 | 0.9 | |||
| Field trips and participation in conferences / seminars / activities | 25 | 0.8 | |||
| Exams | 3 | 0.1 | |||
| Total | 210 | 7 |
Student Assessment
Description
Written final exams witn extended questions and answers to problems to the entire of the material teached (compulsory)
Student Assessment methods
- Written Exam with Extended Answer Questions (Summative)
- Written Exam with Problem Solving (Summative)
Bibliography
Course Bibliography (Eudoxus)
- Εισαγωγή στη Μηχανική Hamilton, Σίμος Ιχτιάρογλου, Κωδικός βιβλίου στον Εύδοξο: 143549999
Last Update
27-08-2025
