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
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.
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:
Important note: Lecture materials provided below may be inclomplete
and should not be considered a substitute for notes taken in class or textbook materials
||Principle of least action. Elements of the calculus of variations.
||Examples of variational problems. General discussion of varitional principles. Euler-Lagrange equation.
||Alternative form of Euler-Lagrange equation (Beltrami equation). Constrained extremization problem. Extending least action principle to systems with constraints. Brachistochrone problem.
||Hamiltonian mechanics. Hamilton's equations of motion.
||Hamiltonian mechanics (continue). Poisson bracket.
||Phase space. Liouville's theorem.
||Virial theorem. Review of basic results for rotational motion of rigid bodies. Tensor of inertia. Displaced axis theorem.
||Moment of inertia about an arbitrary axis. Physical Pendulum.
||Euler angles. Euler equations for a rigid body.
||Torque-free motion of a symmetric top.
||Motion of a symmetric top with one point fixed. Stability of rigid body rotation.
||Two coupled harmonic oscillators. Normal modes. Generalization to the case of n couples harmonic oscillators.
||Forced harmonic oscillator in the Green's function approach.
||Oscillation of n point masses connected by a string. Limit of a continuous string.
||Energy of vibrating string. Wave equation. Method of separation of variables.
||Phase velocity and dispersion.
||Group velocity and wave packets.
||Postulates of Special Theory of Relativity. Lorentz transformation. Transformation of velocities.
||Lorentz transformation as a rotation 4D space-time. Length contraction. Time dilation. Relativistic Doppler effect.
||Relativistic momentum and energy.
||Invariants and 4-vectors. Lagrangian of relativistic free particle.
Found an error on this page or in any of the pdf files? Send an email to the instructor at firstname.lastname@example.org