PHYS 505: Classical Mechanics (graduate) - Fall 2015
Location & Contact Info
Instructor: Sergiy Bubin
Lecture Hours: Mon,Wed,Fri 9:00 AM - 9:50 AM in room 8.319
Recitations: Tue 1:30 PM - 2:45 PM in room 6.518
Office Hours: Mon 2:00 PM - 3:00 PM & Tue 2:50 PM - 3:50 PM, both in room 7.204 (or by appointment)
Phone: +7 (7172) 69 46 63
In this course students learn, at a more advanced level than in the corresponding undergraduate courses, the following topics:
the Lagrangian and Hamilton dynamics, variational calculus, and dynamics of particles and rigid bodies. Modern topics such as
canonical perturbation theory, invariant mappings, nonlinear dynamics and chaos, and applications to semi-classical quantum theory will
also be included as time permits.
H. Goldstein, C. Poole, and J. Safko, Classical Mechanics (3rd Edition)
Other Useful References
Many other texts exist on classical or analytical mechanics both at the introductory and advanced level,
some can be found in the library, and can also be very useful in this course.
Students are encouraged to explore those. Examples of the graduate and/or advanced undergraduate textbooks are:
Homework Submission Guidelines
The submission of only answers is not acceptable. Homework must show
sufficient proof that a derivation of the solution was carried out.
Any student who wants to get the best possible score for his/her homework must:
Homework submission in paper form is strongly preferred. However, electronic submissions
via email (e.g. a pdf file of scanned pages) are acceptable for those students who are
away or must miss a class when the homework is due.
- Staple pages together and clearly indicate problem numbers
- Turn in neat and readable homework as points may be deducted otherwise
- Show work! Solutions or answers turned in without explanation will not receive full credit
*Extended quiz worth twice the points of a regular quiz.
Warning: Lecture materials provided below may be inclomplete
and should not be considered a substitute for notes taken in class or textbook materials
||Review of Newtonian mechanics.
||D'Alembert's principle and Lagrange's equations.
||Velocity-dependent potentials. Dissipation function.
||The principle of the least action. Elements of the calculus of variation.
||General discussion of variational principles. Derivation of Lagrange's equations from the principle of the least action.
||Further discussion of variational problems. Extending the least action principle to systems with constraints.
||Integrating the equations of motion in 1D. Reduction of a two-body problem to the equivalent one-body problem. Equations of motion for a particle in a central field.
||Equation for the orbit in a central field. The Kepler problem.
||Scattering in a central field. Rutherford formula.
||Review of basic results for rotational motion of rigid bodies.
||Review of basic results for rotational motion of rigid bodies (continue).
||Euler equations for the motion of a rigid body.
||Torque-free motion of a symmetric top.
||Stability of rigid body rotation.
||Motion of a symmetric top with one point fixed.
||Review of linear oscillators.
||General approach to a forced harmonic oscillator. Green's function.
||Two coupled harmonic oscillators.
||General case of n coupled harmonic oscillators.
||Oscillation on n point masses connected by a string (a linear array of coupled oscillators).
||Hamiltonian mechanics. Hamilton's equations of motion.
||Hamiltonian mechanics (continue). Canonical transformations.
||Poisson brackets. Liouville's theorem.
||Generating functions for canonical transformations.
Found an error on this page or in any of the pdf files? Send an email to the instructor at firstname.lastname@example.org