Modern Introductory Mechanics Part II

Description

“Modern Introductory Mechanics, Part II” is a continuation of the coverage of topics in classical mechanics found in Part I. The text builds on the previous material and maintains the same spirit of directness and rigor. It is designed to round out the coverage of the important topics in the field, leading to more advanced treatments. Subject matter includes central forces, scattering, non-internal reference frames, rigid bodies, coupled oscillations and special relativity. As in Part I, the many homework problems are directly associated with the development of ideas and topics in the text.

Cover artwork by Gerald Plant.

Content

1. Particle Interactions and Central Forces
   1. Multi-particle conservation laws
   2. Two-body relative coordinates
   3. Runge-Lenz treatment of Coulomb force
   4. Lagrangian equations of motion
   5. Celestial mechanics
   6. General Relativity modification
   7. Orbital stability
   8. Virial theorem
   9. Problems
2. Scattering and Collisions of Particles
   1. Coulomb scattering
   2. Differential cross sections
   3. Rutherford scattering in the center of mass frame
   4. Simple treatment of light deflection
   5. Cross section cookbook
   6. Connection between Lab and CM frames
   7. A kinematical example in the Lab frame
   8. Rutherford scattering in the Lab frame
   9. Total cross section
   10. Problems
3. Non inertial Reference Frames
   1. Finite displacements and rotations
   2. Instantaneous relations for velocity, acceleration
   3. Useful Earth coordinate choices
   4. Deflection of projectiles near Earth’s surface
   5. Deflections for dropped objects
   6. Focault pendulum
   7. Problems
4. Rigid Body Motion
   1. Concept of a rigid body
   2. Instantaneous kinetic energy in body frame
   3. Angular momentum and the inertia tensor
   4. Transformation properties of the inertia tensor
   5. Principal axes
   6. Parallel axis theorem
   7. Euler angles
   8. Euler’s equations of motion
   9. Symmetrical top – Euler solution
   10. Symmetrical top – Lagrangian solution
   11. Problems
5. Coupled Oscillations
   1. Coupled dynamical equations
   2. Eigenvalue/eigenvector solution
   3. Example
   4. Weak/strong coupling
   5. Example using mechanical/electrical analogy
   6. Problems
6. Special Relativity
   1. Invariance and covariance
   2. Two postulates of special relativity
   3. Lorentz tranformations deduced
   4. Alternate notation for Lorentz transformations
   5. The “light cone” and tachyons
   6. Mathematical properties of Lorentz transformations
   7. Consequences of relativity
   8. Velocity addition law
   9. Momentum and energy united
   10. Four short points
   11. Problems