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
Course Description
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.
Course Info
Syllabus: syllabussyllabus.pdf
Required Textbook
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:
  • 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
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.
Homework Assignments
Assignment Problems Due Date Solutions
Homework #1 hwhw01.pdf Sep 25 hwhw01s.pdf
Homework #2 hwhw02.pdf Oct 2 hwhw02s.pdf
Homework #3 hwhw03.pdf Oct 9 hwhw03s.pdf
Homework #4 hwhw04.pdf Oct 28 hwhw04s.pdf
Homework #5 hwhw05.pdf Nov 6 hwhw05s.pdf
Homework #6 hwhw06.pdf Nov 20 hwhw06s.pdf
Homework #7 hwhw07.pdf Dec 4 hwhw07s.pdf
Quiz Date Tasks Solutions
Quiz #1 Sep 28 quizq01.pdf quizq01s.pdf
Quiz #2* Oct 2 quizq02.pdf quizq02s.pdf
Quiz #3 Oct 28 quizq03.pdf quizq03s.pdf
Quiz #4 Nov 16 quizq04.pdf quizq04s.pdf
*Extended quiz worth twice the points of a regular quiz.
  Exam     Date Problems Solutions
Diagnostic test Sep 14 quizdiagnostic.pdf
Midterm #1 Oct 19 quizmt1.pdf quizmt1s.pdf
Midterm #2 Nov 24 quizmt2.pdf quizmt2s.pdf
Final Dec 7 quizfin.pdf quizfins.pdf
Lecture Materials
Warning: Lecture materials provided below may be inclomplete and should not be considered a substitute for notes taken in class or textbook materials
  Lecture        Date   File Topic
Lecture #1 Sep 16 leclec01.pdf Introductory notes.
Lecture #2 Sep 18 leclec02.pdf Review of Newtonian mechanics.
Lecture #3 Sep 21 leclec03.pdf D'Alembert's principle and Lagrange's equations.
Lecture #4 Sep 23 leclec04.pdf Velocity-dependent potentials. Dissipation function.
Lecture #5 Sep 25 leclec05.pdf The principle of the least action. Elements of the calculus of variation.
Lecture #6 Sep 28 leclec06.pdf General discussion of variational principles. Derivation of Lagrange's equations from the principle of the least action.
Lecture #7 Sep 30 leclec07.pdf Further discussion of variational problems. Extending the least action principle to systems with constraints.
Lecture #9 Oct 5 leclec09.pdf 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.
Lecture #10 Oct 6 leclec10.pdf Virial theorem.
Lecture #11 Oct 7 leclec11.pdf Equation for the orbit in a central field. The Kepler problem.
Lecture #12 Oct 9 leclec12.pdf Scattering in a central field. Rutherford formula.
Lecture #13 Oct 21 leclec13.pdf Review of basic results for rotational motion of rigid bodies.
Lecture #14 Oct 23 leclec14.pdf Review of basic results for rotational motion of rigid bodies (continue).
Lecture #15 Oct 28 leclec15.pdf Eulerian angles.
Lecture #16 Oct 30 leclec16.pdf Euler equations for the motion of a rigid body.
Lecture #17 Nov 2 leclec17.pdf Torque-free motion of a symmetric top.
Lecture #18 Nov 4 leclec18.pdf Stability of rigid body rotation.
Lecture #19 Nov 6 leclec19.pdf Motion of a symmetric top with one point fixed.
Lecture #20 Nov 9 leclec20.pdf Review of linear oscillators.
Lecture #21 Nov 11 leclec21.pdf General approach to a forced harmonic oscillator. Green's function.
Lecture #22 Nov 13 leclec22.pdf Two coupled harmonic oscillators.
Lecture #23 Nov 16 leclec23.pdf General case of n coupled harmonic oscillators.
Lecture #24 Nov 18 leclec24.pdf Normal coordinates.
Lecture #25 Nov 20 leclec25.pdf Oscillation on n point masses connected by a string (a linear array of coupled oscillators).
Lecture #26 Nov 23 leclec26.pdf Hamiltonian mechanics. Hamilton's equations of motion.
Lecture #27 Nov 27 leclec27.pdf Hamiltonian mechanics (continue). Canonical transformations.
Lecture #28 Nov 30 leclec28.pdf Poisson brackets. Liouville's theorem.
Lecture #29 Dec 2 leclec29.pdf Generating functions for canonical transformations.
Lecture #30 Dec 4 leclec30.pdf Hamilton-Jacobi equation.

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