Course Identification

1. The Newton equations for one and several particles. Forces and potentials. The Hamiltonian form of the Newton equations. The Poisson brackets.
2. Symmetries and conservations laws. Time and space translations. Rotations. Energy, momentum, and angular momentum. Center of mass. Kinetic and potential energies.
3. One-dimensional motion. Use of energy conservation to obtain a complete solution and its meaning. Simple examples.
4. Two particle problems. Reduced mass. Motion in a central field. The Kepler problem. Classical scattering. Cross-section. Scattering off a Hard Sphere. Rutherford formula.
5. Small oscillations - free and forced. Friction and damped oscillations. Resonance - width and shift. Over damping. Oscillations in systems with many degrees of freedom. Normal modes. Molecular examples. Small oscillations in extended systems and their normal modes. Sound waves as an example.
6. Motion of a rigid body. Angular velocity. Inertia tensor. Angular momentum of a rigid body. Equations of motions and simple solutions.
7. Motion in noninertial frames. Centrifugal and Corriolis forces. Elements of general relativity.
8. (extra topic) Principles of least action. Hamilton vs Fermat. Mechanics as geometrical optics - Hamilton- Jacobi's mechanical analog of the optical eikonal equation.
9. (extra topic) Galilei relativity principle. Elements of relativistic mechanics.

Upon successful completion of this course students should be able to:

1. Demonstrate understanding of the basis of different formulations of classical mechanics and their advantages in addressing different aspects of the description of mechanical systems.
2. Demonstrate familiarity with the all-important connections between conservation laws and world symmetries like symmetries of translation in time and space and rotational symmetry.
3. An improved hands-on experience in dealing with important problems of mechanical systems like systems with constraints, normal modes of mechanical vibrations, motion of rigid bodies, etc.
4. Demonstrate a deep understanding of how non-relativistic mechanics is generalized to include the theory of relativity.

Lectures notes