PH-304 Classical Mechanics

1. Functions, power series representation of an arbitrary function, kinematics, div, grad, curl. Basic theorems (Gauss, Green).
2. Cylindrical and polar coordinates, expressions for velocity and acceleration, coordinate transformations, rotating reference frames.
3. Newton’s laws, momentum, impulse of a force, applications.
4. One-dimensional simple harmonic oscillator, damped SHO, forced SHO, resonance, 3-D SHO, response to several forces applied simultaneously, linear superposition principle.
5. Potential energy, conservative and non-conservative forces.
6. Motion in electromagnetic fields, cyclotron motion, motion in crossed electric and magnetic fields.
7. Rotating coordinate systems, fictitious forces.
8. Angular momentum and central forces, planetary motion under inverse-square force, constants of motion, Kepler’s Laws, orbital transfers and gravitational boosts, radial oscillations about a circular orbit.
9. Systems of particles, motion with a variable mass, rocket motion.
10. Collisions, center of mass frame, elastic and inelastic collisions.
11. Rotations, angular momentum, moment of inertia and theorems, the inertia tensor, principal axes, diagonalization.
12. Principle of least action, Brachistrochrone problem.
13. Generalized coordinates, Lagrangian mechanics, generalized forces, Hamilton’s principle, Hamilton’s equations.
14. Coupled oscillations, normal modes, CO2 oscillation modes.

 
Recommended texts:

• Classical Dynamics of Particles and Systems, by Stephen T. Thornton and Jerry B. Marion, publisher: Brooks Cole; 5th revised edition, (2006).
• Classical Mechanics, by Herbert Goldstein, publisher: Safko and Poole, 3rd Edition (2006).
• Classical Mechanics, by John R. Taylor, publisher: University Science books, (2005).
• Classical Mechanics by L. Chow, publisher John Willey (1995).