Title  ΘΕΩΡΗΤΙΚΗ ΜΗΧΑΝΙΚΗ / Theoretical Mechanics 
Code  ΓΘΥ206 
Faculty  Sciences 
School  Physics 
Cycle / Level  1st / Undergraduate 
Teaching Period  Spring 
Coordinator  Kleomenis Tsiganis 
Common  No 
Status  Active 
Course ID  40002888 
Programme of Study: UPS of School of Physics (2012today)
Registered students: 591
Orientation  Attendance Type  Semester  Year  ECTS 

Core  Compulsory Course  4  2  8 
Academic Year  2019 – 2020 
Class Period  Spring 
Faculty Instructors 

Instructors from Other Categories 

Weekly Hours  5 
Class ID  600159918

Type of the Course
 Background
Course Category
General Foundation
Mode of Delivery
 Face to face
Digital Course Content
 eStudy Guide https://qa.auth.gr/en/class/1/600159918
 At the Website of the School: http://www.physics.auth.gr/courses/5
 Other: http://users.auth.gr/voyatzis/ThMechanics/
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 noninertial reference frames: noninertial 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 degreeoffreedom 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 centralforce fields in Physics: gravity, Coulomb, Yukawa and the twobody 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 leastaction principle and relation to other fields of Physics.
Keywords
Classical Mechanics, Analytical Mechanics
Educational Material Types
 Book
Course Organization
Activities  Workload  ECTS  Individual  Teamwork  Erasmus 

Lectures  117  3.9  ✓  
Reading Assigment  42  1.4  
Tutorial  78  2.6  
Exams  3  0.1  
Total  240  8 
Student Assessment
Student Assessment methods
 Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
1. ΘΕΩΡΗΤΙΚΗ ΜΗΧΑΝΙΚΗ, Ι. ΧΑΤΖΗ∆ΗΜΗΤΡΙΟΥ, Σ. ΓΙΑΧΟΥ∆ΗΣ & ΣIA O.E.
2. ΚΛΑΣΙΚΗ ΜΗΧΑΝΙΚΗ, T.W.B. KIBBLE & F.H. BERKSHIRE, ΙΤΕΠΑΝΕΠΙΣΤΗΜΙΑΚΕΣ ΕΚ∆ΟΣΕΙΣ ΚΡΗΤΗΣ
Additional bibliography for study
Goldstein H. Classical Mechanics, 2nd ed. AddisonWesley, 1980
Sheck Fl. Mechanics, Springer, 1999
Γ.Καραχάλιος, Β. Λουκόπουλος. "Θεωρητική Μηχανική", 2014
Last Update
09062016