Wilcox Walter. Modern Introductory Mechanics Part II

Bookboon, 2016. — 260 p. — ISBN: 978-87-403-1315-4.“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.Particle Interactions and Central Forces
Multi-particle conservation laws
Two-body relative coordinates
Runge-Lenz treatment of Coulomb force
Lagrangian equations of motion
Celestial mechanics
General Relativity modification
Orbital stability
Virial theorem
Problems
Scattering and Collisions of Particles
Coulomb scattering
Differential cross sections
Rutherford scattering in the center of mass frame
Simple treatment of light deflection
Cross section cookbook
Connection between Lab and CM frames
A kinematical example in the Lab frame
Rutherford scattering in the Lab frame
Total cross section
Problems
Non inertial Reference Frames
Finite displacements and rotations
Instantaneous relations for velocity, acceleration
Useful Earth coordinate choices
Deflection of projectiles near Earth’s surface
Deflections for dropped objects
Focault pendulum
Problems
Rigid Body Motion
Concept of a rigid body
Instantaneous kinetic energy in body frame
Angular momentum and the inertia tensor
Transformation properties of the inertia tensor
Principal axes
Parallel axis theorem
Euler angles
Euler’s equations of motion
Symmetrical top – Euler solution
Symmetrical top – Lagrangian solution
Problems
Coupled Oscillations
Coupled dynamical equations
Eigenvalue/eigenvector solution
Example
Weak/strong coupling
Example using mechanical/electrical analogy
Problems
Special Relativity
Invariance and covariance
Two postulates of special relativity
Lorentz tranformations deduced
Alternate notation for Lorentz transformations
The “light cone” and tachyons
Mathematical properties of Lorentz transformations
Consequences of relativity
Velocity addition law
Momentum and energy united
Four short points
Problems