Theoretical Mechanics
| Title | ΘΕΩΡΗΤΙΚΗ ΜΗΧΑΝΙΚΗ / Theoretical Mechanics |
| Code | ΓΘΥ1206 |
| Faculty | Sciences |
| School | Physics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Kleomenis Tsiganis |
| Common | Yes |
| Status | Active |
| Course ID | 600021672 |
Programme of Study: PROGRAMMA SPOUDŌN 2022
Registered students: 185
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| KORMOS | Compulsory Course | 4 | 2 | 9 |
| Academic Year | 2024 – 2025 |
| Class Period | Spring |
| Faculty Instructors |
|
| Weekly Hours | 6 |
| Total Hours | 78 |
| Class ID | 600260374
|
Type Of Offer
- Disciplinary Course
Course Type 2021
General Foundation
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600260374
- At the Website of the School: http://www.physics.auth.gr/courses/5
- eLearning (Moodle): https://elearning.auth.gr/course/view.php?id=6176
Language of Instruction
- Greek (Instruction, Examination)
Prerequisites
General Prerequisites
Good prior knowledge in General Physics I, Differential and Integral calculus is recommended
Learning Outcomes
In the end of the lectures, the students
1) should have understood the fundamental laws of Mechanics and the rigorous mathematical framework that describes these laws and produces the new knowledge in the particular scientific field.
2) should be able to understand in details and build part of the theory based on the fundamental laws and by using mathematics
3) should have got advanced studies passing from the classical Newtonian approximation to the Lagrangian Mechanics and the modern Hamiltonian Mechanics.
4) should become familiar with new advanced methods for modeling and managing complicated mechanical systems, constructing the equations of motion and finding first integrals.
General Competences
- Apply knowledge in practice
- Generate new research ideas
Course Content (Syllabus)
1. Newtonian mechanics: axioms, laws of dynamics and vector form of the differential equations of motion. Conservation laws.
2. Motion in intertial and non-inertial reference frames: non-inertial forces and equations of motion. Examples.
3. Coordinate systems: differential equation of motion in cartesian, spherical and cylindrical coordinates. Examples.
4. Dynamics: equilibria and their stability. Study of conservative 1 degree-of-freedom system, using the method of Potential. Phase diagrams.
5. Applications to 1 d.o.f systems: harmonic oscillator, pendulum, systems with friction, forced oscillations.
6. Central forces: conservation of angular momentum, effective potential and study of the equivalent 1 d.o.f system
7. Solutions of the equations of motion for basic central-force fields in Physics: gravity, Coulomb, Yukawa and the two-body problem.
8. Analytical mechanics: constraints and reaction forces – degrees of freedom. Classification of mechanical systems. Principle of virtual work.
9. The d'Alembert principle and Lagrange's equations: the Lagrangean function for conservative forces (scalar and vector potentials). Examples
10. Applications: finding equations of motion and conserved quantities (integrals of motion) with Lagrange's method.
11. The analytical method of Hamilton: The Hamiltonian function, canonical equations, phase space and integrals of motion. Applications.
12. The principle of least action: Hamilton's principle and axiomatic foundation of mechanics. Physical importance of the least-action principle and relation to other fields of Physics.
Keywords
Classical Mechanics, Analytical Mechanics
Educational Material Types
- Multimedia
- Book
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Communication with Students
- Use of ICT in Student Assessment
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 120 | 4 | |||
| Reading Assigment | 110 | 3.7 | |||
| Tutorial | 34 | 1.1 | |||
| Exams | 6 | 0.2 | |||
| Total | 270 | 9 |
Student Assessment
Student Assessment methods
- Written Exam with Multiple Choice Questions (Formative)
- Written Exam with Short Answer Questions (Formative)
- Written Exam with Extended Answer Questions (Formative, Summative)
- Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
1. Κλασική Δυναμική Σωματιδίων και Συστημάτων, Thornton T. Stephen,Marion B. Jerry,επιμ Καντή Π, Χωρίκης Θ, 2020, Έκδοση: 1η, Εκδόσεις: Gutenberg, ISBN: 9789600121506, [Κωδικός στον Εύδοξο: 94644129]
2. Θεωρητική Μηχανική, Καραχάλιος Γεώργιος , Λουκόπουλος Βασίλειος, 2014, Έκδοση: 1, Εκδόσεις: Liberal Books, ISBN: 9786188008472, [Κωδικός στον Εύδοξο: 50659220]
3. ΘΕΩΡΗΤΙΚΗ ΜΗΧΑΝΙΚΗ, ΧΑΤΖΗΔΗΜΗΤΡΙΟΥ ΙΩΑΝΝΗΣ, 2013, Έκδοση: 1, Εκδόσεις: ΓΙΑΧΟΥΔΗ, ISBN: 9789606700996, [Κωδικός στον Εύδοξο: 33153244]
Additional bibliography for study
Νευτώνια Μηχανική, Π. Ιωάννου, Θ. Αποστολάτος, εκδόσεις Κάλλιπος
Last Update
18-07-2025
