2020-2021   Academic Year     Spring Semester


PHYSICS 218   Analytical Mechanics


schedule:         monday 15:30   & 16:30     thursday 10:30 & 11:30    


TEXTBOOK:     Classical Dynamics of Particles and Systems,     authors: Thornton S & Marion J

the course assistant: Mustafa Kahraman     ...

ACADEMIC CALENDAR


lecture notes
01 02 03 04 05 06 07 xx 08



course content
SYLLABUS (tentative) Vectors and vector fields, products of vectors, line integral of a vector field, concept of scalar potential, surface and volume integrals of vector fields, divergence and Stoke's theorems, Greenís identities, particle kinematics, rotation of coordinate axes, invariants under rotations, curvilinear coordinates: plane polar, cylindrical and spherical polar coordinates, vector derivatives: velocity and acceleration vectors expressed in terms of polar coordinates, concept of angular velocity Newtonian mechanics: some examples of particle dynamics, retarding forces, motion under frictional drag force, periodic motion, harmonic and an-harmonic oscillators, conservative property of an oscillator, damped oscillator, under- and over-damped motions, effect of a harmonic driving force on a damped oscillator, resonant behavior Coupled oscillators with two degrees of freedom, normal modes of oscillation and the relevant characteristic frequencies, the role the boundary conditions play on the characteristic modes of oscillation, two dimensional oscillator with linked coordinates, phenomenon of beats Classical wave equation, transverse vibrations on strings and membranes, variational approximations to estimate the eigenfrequencies Wave equation pertaining to oscillations in non-homogeneous media; examples: lateral vibrations of a hanging chain, transverse vibrations along a rope spun about one end; Bessel functions or Legendre polynomials as characteristic descriptions of vibration, Oscillatory systems with many degrees of freedom, Continuous systems, sinusoidal and exponential waves Gravitation and gravitational potential, Central force motion Dynamics of a system of particles, the centre of mass concept, elastic and inelastic collisions Calculus of variations, Euler's equations, the Brachistochrone problem Hamilton's principle, Lagrange's equations of motion in generalised coordinates, Hamiltonian's equations of motion, Lagrangian and Hamiltonian dynamics: examples Rigid body dynamics, inertia tensor, principle axes of inertia, Euler's equations of motion for a rigid body


supplements

volume of a parallelepiped
the cross product: Ax(BxC)
vector identities
explicit forms of vector operations
rotations do not commute
rotation of coordinate axes
velocity and acceleration in uniform circular motion
motion in polar coordinates
anharmonic oscillator - perturbation treatment



grading
first exam     second exam     final exam     other    
25% 25% 25% 25%


exam dates
first exam   March 11 Thursday @ 10:30
second exam       April 19 Thursday @ 10:30
final exam May @







final exam qualification criteria
If the sum of the two midterm grades lies below 50,
or have a poor attendance rate to the lectures (<65%),
you will not be admitted to the final exam and receive an FZ grade.


useful links




Isaac Newton
Euler