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PHYS 5103: Advanced Mechanics

PHYS 5103: Advanced Mechanics (Fall 2016, University of Arkansas). 2016 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.

1st Axioms and Theorems of Classical Mechanics


Lecture 01 - 1st Axioms and Theorems of Classical Mechanics
Lecture 02 - Analysis of 1D 2-Body Collisions I
Lecture 03 - Analysis of 1D 2-Body Collisions II: Reflection Groups
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
Lecture 07 - Kepler Geometry of Isotropic Harmonic Oscillator (IHO) Elliptical Orbits
Lecture 08 - Quadratic Form Geometry and Development of Mechanics of Lagrange and Hamilton
Lecture 09 - Equations of Lagrange and Hamilton Mechanics in Generalized Curvilinear Coordinates (GCC)
Lecture 10 - Hamiltonian vs. Lagrange Mechanics in Generalized Curvilinear Coordinates (GCC)
Lecture 11 - Poincare, Lagrange, Hamiltonian, and Jacobi Mechanics
Lecture 12 - Complex Variables, Series, and Field Coordinates I
Lecture 13 - Complex Variables, Series, and Field Coordinates II
Lecture 14 - Introducing GCC Lagrangian a la Trebuchet Dynamics
Lecture 15 - GCC Lagrange and Riemann Equations for Trebuchet
Lecture 16 - Hamilton Equations for Trebuchet and Other Things
Lecture 17 - Riemann-Christoffel Equations and Covariant Derivative
Lecture 18 - Electromagnetic Lagrangian and Charge-field Mechanics
Lecture 19 - Classical Constraints: Comparing Various Methods
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
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 2016)
Text Topics for Units 1-8. Lecture Slides. Assignments and Solutions. Related Papers and Talks.