PHYS 222 Classical Mechanics II (Spring 2019)

Location & Contact Info
Instructor: Sergiy Bubin
Lecture Hours: Tue,Thu 10:30am - 11:45am in room 7.317
Recitations: Tue 12:00pm - 1:15pm in room 7.317
Office Hours: Thu 12:30pm - 1:30pm and 5:30pm-6:30pm in room 7E.333, or by appointment
Phone: +7 (7172) 694663
Course Description
This course aims to cover the following topics: the Lagrangian, Hamilton, and Hamilton-Jacobi dynamics, canonical transformations, variational calculus and the least action principle, dynamics of particles and rigid bodies, Green's functions, oscillations and normal coordinates. The relativistic dynamics, fluid dynamics, nonlinear dynamics and chaos may be considered as time permits. The course will include two lectures per week accompanied by a recitation.
Course Info
Syllabus: syllabussyllabus.pdf
Main Textbook
S. Thornton and J. Marion, Classical Dynamics of Particles and Systems (5th Edition)
Other Useful References
Many other texts exist on classical mechanics at the introductory (undergraduate) level, some can be found in the library, and can also be very useful in this course. Students are encouraged to explore those. Examples are:
Homework Assignments
Assignment Problems Due Date Solutions
Homework #1 hwhw01.pdf Jan 24 hwhw01s.pdf
Homework #2 hwhw02.pdf Jan 31
Homework #3 hwhw03.pdf Feb 14
Homework #4 hwhw04.pdf Feb 28
Homework #5 hwhw05.pdf April 9
Homework #6 hwhw06.pdf April 19
Quiz Date Tasks Solutions
Quiz #1 Jan 22 quizq01.pdf quizq01s.pdf
Quiz #2 Jan 29 quizq02.pdf quizq02s.pdf
Quiz #3 Feb 14 quizq03.pdf quizq03s.pdf
Quiz #4 Feb 26 quizq04.pdf quizq04s.pdf
Quiz #5 Apr 2 quizq05.pdf quizq05s.pdf
  Exam     Date Problems Solutions
Diagnostic Test Jan 8 examdiag.pdf
Midterm #1 Feb 5 exammt1.pdf exmmt1s.pdf
Midterm #2 Mar 12 exammt2.pdf exammt2s.pdf
Midterm #3 Apr 9 exammt3.pdf exammt3s.pdf
Final Apr 24 examfin.pdf examfins.pdf
Lecture Materials
Important note: 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 Jan 10 leclec01.pdf Principle of least action. Elements of the calculus of variations.
Lecture #2 Jan 15 leclec02.pdf Examples of variational problems. General discussion of varitional principles. Euler-Lagrange equation.
Lecture #3 Jan 17 leclec03.pdf Alternative form of Euler-Lagrange equation (Beltrami equation). Constrained extremization problem. Extending least action principle to systems with constraints. Brachistochrone problem.
Lecture #4 Jan 22 leclec04.pdf Hamiltonian mechanics. Hamilton's equations of motion.
Lecture #5 Jan 24 leclec05.pdf Hamiltonian mechanics (continue). Poisson bracket.
Lecture #6 Jan 29 leclec06.pdf Phase space. Liouville's theorem.
Lecture #7 Jan 31 leclec07.pdf Virial theorem. Review of basic results for rotational motion of rigid bodies. Tensor of inertia. Displaced axis theorem.
Lecture #8 Feb 7 leclec08.pdf Moment of inertia about an arbitrary axis. Physical Pendulum.
Lecture #9 Feb 12 leclec09.pdf Euler angles. Euler equations for a rigid body.
Lecture #10 Feb 14 leclec10.pdf Torque-free motion of a symmetric top.
Lecture #11 Feb 19 leclec11.pdf Motion of a symmetric top with one point fixed. Stability of rigid body rotation.
Lecture #12 Feb 21 leclec12.pdf Two coupled harmonic oscillators. Normal modes. Generalization to the case of n couples harmonic oscillators.
Lecture #13 Feb 26 leclec13.pdf Normal coordinates.
Lecture #14 Feb 28 leclec14.pdf Forced harmonic oscillator in the Green's function approach.
Lecture #15 Mar 14 leclec15.pdf Oscillation of n point masses connected by a string. Limit of a continuous string.
Lecture #16 Mar 26 leclec16.pdf Energy of vibrating string. Wave equation. Method of separation of variables.
Lecture #17 Mar 28 leclec17.pdf Phase velocity and dispersion.
Lecture #18 Apr 2 leclec18.pdf Group velocity and wave packets.
Lecture #19 Apr 4 leclec19.pdf Postulates of Special Theory of Relativity. Lorentz transformation. Transformation of velocities.
Lecture #20 Apr 11 leclec20.pdf Lorentz transformation as a rotation 4D space-time. Length contraction. Time dilation. Relativistic Doppler effect.
Lecture #21 Apr 16 leclec21.pdf Relativistic momentum and energy.
Lecture #22 Apr 18 leclec22.pdf Invariants and 4-vectors. Lagrangian of relativistic free particle.

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