Classical Mechanics 111A
(47520)
Fall 2009
Lectures:
When:
Tuesday & Thursday,
2:00--3:20pm. Where:
ELH
110
Discussions:
When: Monday, 1:00--1:50pm
Where: RH
108
Instructor: Sasha Chernyshev,
Associate
Professor
Office: RH 310F
Phone: (949)-824-6440
E-mail: sasha@uci.edu
Web page: http://www.physics.uci.edu/faculty/chernyshev.html
Office Hours:
Mon. 2:00-4:00pm, Fri. 2:00-4:00pm
Textbook
- S. T. Thornton and J. B. Marion, Classical Dynamics of
Particles and Systems, 5th edition.
The course will cover Chapters 2-8. Lectures will sometimes use
alternative sources.
Subject
This course is the first in the 2-quarter sequence on the Classical
Mechanics. It is a course in theoretical physics.
There are two main parts of the 111A course: Newtonian mechanics (aka
solving equations of motion) and
Lagrangian/Hamiltonian formalism.
Here is a rough list of topics to be covered (to be updated):
- Newtonian mechanics
- Reminder
- Newton's laws
- Equation of motion
- differential equations
- Resistive forces, 1D, 2D, see maple
output
- perturbative methods
- to the aestetic value and use of characteristic scales
- use of dimensionless notations
- motion in a magnetic field, cyclotron frequency, etc.
- Energy, momentum conservation
- free fall of a meteor, escape velocity
- particle motion in a "potential landscape"
- confined, deconfined, stable/unstable equilibrium, turning
points
- integration of the equation of motion, examples:
- 1D motion in the gravity field
- harmonic oscillator
problem
- -x^4 potential,
behavior at infinity
- Morse potential,
oscillations and deconfinement, see graphs
- Perturbartion theory around the "known" solution
- Oscillations
- Harmonic oscillator, generality of the problem
- Newton's perspective, returning force (linear force), 2nd
order DE
- Potential perspective, energy conservation, 1st order DE
- Phase space, phase diagram
- Pendulum as an example of the constrained motion
- -- general equation
- -- small oscillations solution
- -- solution for any amplitude
- -- Elliptic integral, period, perturbative
expansion
- -- anharmonicities
- -- infinite period for the unstable
equilibrium point
- -- phase diagram, attractors,
separatrix, + potential profile
- Isochronous pendulum problem
- -- solution, equation of a curve, cycloid
- Damped oscillations
- -- underdamped, frequency shift
- -- overdamped
- -- critically damped
- general solution, solution for the critical case
- energy consideration
- phase diagrams for all the cases
- examples
- Driven systems
- periodic force, steady-state solution
- resonance, Q-factor, width, resonance frequency
- phase lag, closing onto resonant frequency by measuring it
- energy dissipation
- independence of Fourier harmonics, superposition principle
- oscillator driven by non-harmonic forces
- -- "selection" of the resonant harmonics
- Notion of the chaos
- -- relation to non-linearity
- -- Lyapunov's exponent
- -- example: double pendulum
- Central forces
- Gravity law by Newton, universality
- "electrostatic" parallels, finite-size bodies
- Gravitational potential, gravitational force field
- -- force field of a sphere
- -- outside
- -- inside
- Potential energy, explicit proof of conservative nature of
the central force
- -- potential of a ring
- Potential inside a body, Gauss theorem
- Motion in central field
- Conservation of the angular momentum
- Kepler's 1,2,3 laws
- Areal law = conservation of the momentum -- any central field
- Energy equation of the orbit, Energy conserving approach
- Kepler-like problems (deducing force from the orbit)
- -- example of a spiral
- Newton-equation approach
- -- another derivation of the
angular momentum conservation
- -- force-equation of the orbit
- -- more about the spiral
- 1/r^2 force
- -- deducing orbit equation from the given force
using force-equation of the orbit
- -- deducing orbit equation from the given
potential using energy-equation of the orbit
- analysis of the solution:
- -- closed, open
- -- bounded, unbounded
- -- conic sections: circle, ellipse,
parabola, hyperbola
- Geometric properties of the elliptic orbits, their
characteristics
- -- eccentricity, major/minor axes,
peri-/apo- centers
- -- their relations to the energy and
angular momentum
- -- their relations to the initial
conditions
- Effective potential energy, potential energy profile
- -- relation to the type of orbit
- Examples
- etc.
- Calculus of variations
- Euler
- Problems with constraints
- Lagrange/Hamiltonian Dynamics
- Euler-Lagrange
- Generalized coordinates
- Canonical equation of motion
- etc....
Assignments/Exams
There will be weekly homework assignments, midterm, and a final.
The grade for
the course will be based on: (i)
homework (35%)
(ii)
midterm
(30%)
(iii) final exam
(35%)
Homeworks will be assigned weekly and will consist of the reading
assignment and problems to solve.
The homeworks
are due on Tuesdays,
before the lecture, or earlier, if you cannot attend it for any
reason.
Working in groups is encouraged, but each students needs to hand in
their own solutions.
The midterm
exam will be held on Thursday,
October 29, during the lecture time.
The comprehensive Final exam
is scheduled for Thursday,
December 10, 1:30 pm - 3:30 pm
in the same lecture hall -- ELH 110.
Sample exams can be found in the web-page of the previous year course
by a different instructor.
They may, or may not, reflect the scope and the difficulty of this year
exams.
There is no makeup for the homework, midterm or final.
Academic Honesty
Please review the campus
policy on academic honesty which applies to this course.
Cheating on any exam or homework will result in an automatic failure of
the course.
In addition,
the appropriate Deans will be notified.