## General

Code: ΓΘΥ206

Semester: 4

Hrs/week: 5

ECTS Credits: 8

## Content

·
Newtonian mechanics:
axioms, laws of dynamics and vector form of the differential equations of
motion. Conservation laws.

·
Motion in inertial
and non-inertial reference frames: non-inertial forces and equations of motion.
Examples.

·
Coordinate systems:
differential equation of motion in cartesian, spherical and cylindrical
coordinates. Examples.

·
Dynamics: equilibria
and their stability. Study of conservative 1 degree-of-freedom system, using
the method of Potential. Phase
diagrams.

·
Applications to 1
d.o.f systems: harmonic oscillator, pendulum, systems with friction, forced
oscillations.

·
Central forces:
conservation of angular momentum, effective potential and study of the
equivalent 1 d.o.f system

·
Solutions of the
equations of motion for basic central-force fields in Physics: gravity,
Coulomb, Yukawa and the two-body problem.

·
Analytical mechanics:
constraints and reaction forces – degrees of freedom. Classification of
mechanical systems. Principle of virtual work.

·
The d'Alembert
principle and Lagrange's equations: the Lagrangian function for conservative
forces (scalar and vector potentials). Examples

·
Applications: finding
equations of motion and conserved quantities (integrals of motion) with
Lagrange's method.

·
The analytical method
of Hamilton: The Hamiltonian function, canonical equations, phase space and
integrals of motion. Applications.

·
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.

·
Summary
and Discussion

## Suggested literature:

## Additional suggested literature:

- Goldstein H. Classical Mechanics, 2nd ed. Addison-Wesley, 1980
- Sheck Fl. Mechanics, Springer, 1999

## Teacher(s)