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PHYS 5103: Advanced Mechanics

PHYS 5103: Advanced Mechanics (Fall 2015, University of Arkansas). 2015 Fall Physics Lectures from the University of Arkansas - Fayetteville, AR. These videos are a component of the graduate course PHYS 5103 - "Advanced Mechanics" using the text "Classical Mechanics with a Bang!", both developed by Prof. William G. Harter. The class provides a geometric approach to classical mechanics. Geometry helps to clarify the calculus and physics of mechanics and shows that the symmetry principles behind classical theory also underlie quantum theory.

Axiomatic Development of Classical Mechanics


Lecture 01 - Axiomatic Development of Classical Mechanics
Lecture 02 - Analysis of 1D 2-Body Collisions I
Lecture 03 - Analysis of 1D 2-Body Collisions II
Lecture 04 - Kinetic Derivation of 1D Potentials and Force Fields
Lecture 05 - Dynamics of Potentials and Force Fields
Lecture 06 - Geometry of Common Power-law Potentials I
Lecture 07 - Geometry of Common Power-law Potentials II
Lecture 08 - Kepler Geometry of Isotropic Harmonic Oscillator (IHO) Elliptical Orbits
Lecture 09 - Quadratic Form Geometry and Development of Mechanics of Lagrange and Hamilton
Lecture 10 - Equations of Lagrange and Hamilton Mechanics in Generalized Curvilinear Coordinates (GCC)
Lecture 11 - Hamiltonian vs. Lagrange Mechanics in Generalized Curvilinear Coordinates (GCC)
Lecture 12 - Poincare, Lagrange, Hamiltonian, and Jacobi Mechanics
Lecture 13 - Complex Variables, Series, and Field Coordinates I
Lecture 14 - Complex Variables, Series, and Field Coordinates II
Lecture 15 - Introducing GCC Lagrangian a la Trebuchet Dynamics
Lecture 16 - GCC Lagrange and Riemann Equations for Trebuchet
Lecture 17 - Hamilton Equations for Trebuchet and Other Things
Lecture 18 - Riemann-Christoffel Equations and Covariant Derivative
Lecture 19 - Electromagnetic Lagrangian and Charge-field Mechanics
Lecture 20 - Introduction to Classical Oscillation and Resonance
Lecture 21 - Introduction to Coupled Oscillation and Eigenmodes
Lecture 22 - Introduction to Spinor-Vector Resonance Dynamics
Lecture 23 - U(2)~R(3) Algebra/Geometry in Classical or Quantum Theory
Lecture 24 - Parametric Resonance and Multi-particle Wave Modes
Lecture 25 - Introduction to Orbital Dynamics
Lecture 26 - Geometry and Symmetry of Coulomb Orbital Dynamics I
Lecture 27 - Geometry and Symmetry of Coulomb Orbital Dynamics II
Lecture 28 - Multi-particle and Rotational Dynamics
Lecture 29 - Classical Constraints: Comparing Various Methods
Lecture 30 - Relawavity and a Novel Introduction to Relativistic Mechanics I
Lecture 31 - Relawavity and a Novel Introduction to Relativistic Mechanics II

References
Classical Mechanics with a Bang! (Fall 2015)
Lecture Slides. Lecture 1. Axiomatic Development of Classical Mechanics. Lecture 2. Analysis of 1D 2-Body Collisions I. Lecture 3. Analysis of 1D 2-Body Collisions II. ...