# Theoretical Mechanics

 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

 Academic Year 2017 – 2018 Class Period Spring Faculty Instructors Kleomenis Tsiganis 52hrs Georgios Vougiatzis 52hrs Instructors from Other Categories Kosmas Kosmidis 26hrs Vasileios Oikonomou 52hrs Weekly Hours 5 Class ID 600100215
Course Type 2016-2020
• Background
Course Type 2011-2015
General Foundation
Mode of Delivery
• Face to face
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
• Book
Course Organization
Lectures117