Compulsory

Theoretical Mechanics

CODE
ΓΘΥ206
SEMESTER
4
HOURS per WEEK
5
ECTS CREDITS
8
INSTRUCTORS

Georgios Vougiatzis

Kleomenis Tsiganis

Kosmas Kosmidis

·       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

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