| Week 1 | |
| Wednesday, September 4 | Introductory Lecture |
| Friday, September 6 | LL 1.2 The principle of minimal action, Lagrange's equation |
| Week 2 | |
| Monday, September 9 | LL 1.3 Galileo's relativity principle, LL 1.4 The Lagrangian for a free particle: substitute lecture by Prof. Jay Sau |
| Wednesday, September 11 | LL 1.5 The Lagrangian for a system of particles, LL 2 Conservation Laws: substitute lecture by Prof. Jay Sau |
| Friday, September 13 | LL 2 Conservation Laws: substitute lecture by Prof. Jay Sau |
| Week 3 | |
| Monday, September 16 | LL 2.10 Mechanical similarity and scaling; GPS 3.4 The virial theorem |
| Wednesday, September 18 | GPS 2.4, LL 6.38 Lagrange equations with constraints, reaction forces,
GPS 2.2 Calculus of variations; Statics as minimization of potential energy;
HW 1 issued (Lagrange Equations and Conservation Laws) |
| Friday, September 20 | Catenary and arches; Energy, energy function, and Hamiltonian; LL 3.11 Motion in one dimension |
| Week 4 | |
| Monday, September 23 | LL 7.40, GPS 8.1 Hamilton's equations of motion; Legendre transformation |
| Wednesday, September 25 | LL 7.41, GPS 8.2-3 The Routhian; elimination of cyclic variables;
HW 2 issued (Hamiltonian formalism) |
| Friday, September 27 | LL 7.42, GPS 9.5-7 Poisson brackets, canonical quantization; LL 7.43 The action as a function of coordinates; Feynman's path integrals formulation of quantum mechanics in a Lagrangian form |
| Week 5 | |
| Monday, September 30 | LL 7.43, GPS 8.5 Variational principle for Hamilton's equation of motion; LL 7.45, GPS 9.1 Canonical Transformations |
| Wednesday, October 2 | LL 7.46, GPS 9.9 Liouville's theorem;
GPS 9.4 Symplectic dynamics in phase space;
HW 3 issued (Hamiltonian formalism) |
| Friday, October 4 | Liouville's theorem in statistic physics; LL 7.49, GPS 12.5 Adiabatic invariants in classical mechanics, Adiabatic approximation in quantum mechanics |
| Week 6 | |
| Monday, October 7 | LL 3.13 The reduced mass; LL 3, GPS 3 The Central Force Problem; Kepler's Problem |
| Wednesday, October 9 | GPS 3.9 The Laplace-Runge-Lenz vector; elliptic orbits;
HW 4 issued (The Central Force Problem) |
| Friday, October 11 | GPS 3.10-12, LL 4, Scattering in a central potential; Rutherford's formula |
| Week 7 | |
| Monday, October 14 | GPS 3.11, LL 4 Transformation of the scattering problem to laboratory coordinates |
| Wednesday, October 16 | Motion of a Rigid Body;
LL 6.31 Angular velocity; LL 6.32, GPS 5.1-4 The inertia tensor;
HW 5 issued (Collisions between particles; Tensor of Inertia) |
| Friday, October 18 | 6.33 Angular momentum of a rigid body; GPS 5.2 Tensors; Properties of tensors: contraction, invariance, covariance; GPS 4.2 Orthogonal transformations; GPS 4.3 Formal properties of the transformation matrix of rotation |
| Week 8 | |
| Monday, October 21 | Invariance of length and the Kronecker-delta tensor; Coordinate system transformation to principal axes of inertia; Principal moments of inertia |
| Wednesday, October 23 | Invariance of volume and the antisymmetric tensor;
HW 6 issued (The Kinematics of Rigid Body Motion) |
| Friday, October 25 | GPS 4.8 Infinitesimal rotations; Generators of rotation; Lie algebra; SO(3) group commutation relations |
| Week 9 | |
| Monday, October 28 | Abelian SO(2), U(1) and non-Abelian SO(3), SU(2) groups, spinors;
Parity and inversion, axial and polar vectors, pseudotensors, parity violation in nature |
| Wednesday, October 30 | GPS 4.4, LL 6.35 Euler's angles; Angular velocity in terms of Euler's angles |
| Friday, November 1 | Midterm exam:
In-class open-book exam - you can use the textbooks and your notes.
This exam will cover LL Ch. 1-4 and 7, GPS Ch. 1-3 and 8-9,
HW 1-5 up to but not including Rigid Body Motion.
Prof. Yakovenko will be away, and graduate student Sergey Pershoguba will proctor at the midterm exam. |
| Week 10 | |
| Monday, November 4 | LL 6.33, 6.35 Free motion of a symmetric top; LL 6.34 Torque |
| Wednesday, November 6 | LL problems 6.35, GPS 5.7: Motion of a spinning top subject to
gravitational torque, precession and nutations;
Stability of the vertical spinning of a top;
HW 7 issued (The Rigid Body Equations of Motion) |
| Friday, November 8 | LL 6.38 Rigid bodies in contact, non-slip rolling, reaction forces and torques; LL 6.31 The instantaneous axis of rotation |
| Week 11 | |
| Monday, November 11 | GPS 5.5, LL 6.36 Euler's equations of motion; LL 6.37, GPS 5.6 Motion of asymmetric top |
| Wednesday, November 13 | GPS 4.9 Rate of change of a vector;
LL 6.39, GPS 4.10 The Coriolis force;
cyclones and jet streams in the atmosphere of rotating Earth
HW 8 issued (Rotational Motion) |
| Friday, November 15 | LL 6.39 Motion in a non-inertial reference frame;
GPS 1.5 Lorentz force and motion in electromagnetic field;
GPS 5.9 Precession of electric charges in a magnetic field: gyromagnetic ratio, Larmor theorem |
| Week 12 | |
| Monday, November 18 | LL 5.21-5.23, GPS 6.1-6.3, Small oscillations; Normal modes; LL 5.24, GPS 6.4 Vibrations of a triatomic molecule CO2 |
| Wednesday, November 20 | Vibrations of a 1D crystal; Phonon dispersion relation;
HW 9 issued (Small Oscillations) |
| Friday, November 22 | Phonon dispersion relation; Continuous limit of a 1D crystal; acoustic waves |
| Week 13 | |
| Monday, November 25 | Wave equation in 1D; Continuous elastic medium in 3D: strain tensor |
| Wednesday, November 27 | Elastic modulus tensor; Lamé coefficients;
Equations of motion for continuous medium;
HW 10 issued (Theory of Elasticity) |
| Friday, November 29 | Thanksgiving Holiday, no lecture |
| Week 14 | |
| Monday, December 2 | Stress tensor; GPS 7 Special Relativity; Handout: Lorentz transformation as a hyperbolic rotation derived from the group property of transformations |
| Wednesday, December 4 | The invariant speed;
Invariance of the interval;
Time-like and space-like intervals;
Rapidity and relativistic addition of velocities;
HW 11 issued (Theory of Relativity) |
| Friday, December 6 | Minkowski metric tensor; Covariant and contravariant 4-vectors; Relativistic action for a free particle |
| Week 15 | |
| Monday, December 9 | Relativistic energy and momentum; 4-velocity and 4-momentum; GPS 7.7 Relativistic collisions |
| Wednesday, December 11 | 4-potential of an electromagnetic field; Relativistic action for a charged particle in an electromagnetic field; GPS 7.6 Equations of motion in an electromagnetic field |
| Friday, December 13
update point |
Tensor of the electromagnetic field; Action for the electromagnetic field; Maxwell's equations as the Lagrange equations for the electromagnetic field |
| Final Exam | |
| Thursday, December 19, 8-10 am | Open book exam - you can use the textbook and your notes. The exam will be in the usual room 1402. |
Last updated December 16, 2013