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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.

Lecture 18 - Riemann-Christoffel Equations and Covariant Derivative

Lecture Slides

Lecture 18. Riemann-Christoffel Equations and Covariant Derivative

Go to the Course Home or watch other lectures:

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