Summary of lecture notes:

. To directory listing

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• Lecture 1 [Aug/30] : Welcome and Review of Newtonian Mechanics
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• Lecture 2 [Sep/04] : Conservation laws; Methods for F(t), F(v)
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• Lecture 3 [Sep/06] : Sample F(v); Bound/Unbound Motions in Potential V(x)
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• Lecture 4 [Sep/9] : Motion in V(x): Turning points, Speed, Plots and Roller Coasters
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• Lecture 5 [Sep/11] : Motion Near Equilibrium; Quantitative Potential Methods
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• Lecture 6 [Sep/13] : Sample: SHM from Potential Methods; Phasors and D.E.'s
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• Lecture 7 [Sep/16] : More on D.E.'s; SHO examples
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• Lecture 8 [Sep/18] : Intro, Damped Harmonic Oscillator
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• Lecture 9 [Sep/20] : Critical Damping; Intro, Driven Harmonic Oscillator
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• Lecture 10 [Sep/23] : Resonance; Intuition on Taylor Expansions
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• Lecture 11 [Sep/25] : Full solutions and Fourier series; Intro Multidimensional Mechanics
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• Lecture 12 [Sep/27] : Acceleration in Components: Polar and Spherical Coordinates
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• Lecture 13 [Sep/30] : 3-d Complications; The Work-energy theorem and potential in 3-d
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• Lecture 14 [Oct/02] : Evaluating loop integrals; Stokes' theorem, Curl and the Gradient
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• Lecture 15 [Oct/04] : More on Gradients; Conservative Forces as Gradients
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• Lecture 16 [Oct/07] : Drawbacks of Newtonian formalism; General Coordinate Transformations of Newton II
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• Lecture 17 [Oct/09] : Euler-Lagrange from Newton II
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• Lecture 18 [Oct/11] : Examples and Advantage of Lagrangian Approach (Pendulum, Bead on Wire)
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• Lecture 19 [Oct/16] : Intro to Variational Calculus
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• Lecture 20 [Oct/18] : Euler-Lagrange from Variational Principles; Hamilton's principle; the Jacobi integral
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• Lecture 21 [Oct/21] : Example Problem: Geodesics on the Sphere
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• Lecture 22 [Oct/23] : Variational Problems, Generalizations and Constraints
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• Lecture 23 [Oct/25] : Example Constrained Extremization Problems; Geometry
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• Lecture 24 [Oct/28] : Constrained Problems in Variational Calculus and Mechanics
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• Lecture 25 [Oct/30] : Heuristics, Degrees of Freedom, Proper and Overcomplete sets of coordinates
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• Lecture 26 [Nov/01] : Example: Motion and Tension of Spherical Pendulum
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• Lecture 27 [Nov/04] : Example: Motion and Friction, Disk Rolling without Slipping on Incline Plane
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• Lecture 28 [Nov/06] : Comments on Constraints; Intro to Symmetries and Conservation Laws
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• Lecture 29 [Nov/08] : Galilean Group; Noether's Theorem
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• Lecture 30 [Nov/11] : Noether's Theorem Examples
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• Lecture 31 [Nov/13] : Hamiltonian Mechanics; Intro to Central Force Motion
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• Lecture 32 [Nov/18] : The Central Force Effective Potential
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• Lecture 33 [Nov/20] : Qualitative Central Force Motion; Circular and Near-Circular Orbits
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• Lecture 34 [Nov/22] : Integral Solutions; Orbit Equation; Solution and Energetics for Gravitational Interaction
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• Lecture 35 [Nov/25] : The Geometry of Gravitational Orbits
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• Lecture 36 [Nov/27] : Kepler's Laws; Rutherford Scattering and Repulsive Coulomb orbits
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• Lecture 37 [Dec/02] : Intro to Multiparticle Systems: Separating Center of mass and relative motion; Translational and Rotational (Euler) Equations
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• Lecture 38 [Dec/04] : Intro to Rigid Bodies: Euler's theorem, Space and Body fixed frames, Fictitious Forces
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• Lecture 39 [Dec/06] : Rigid bodies with one point fixed: Angular Momentum and the Inertia Tensor
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• Lecture 40 [Dec/09] : Principal Axes; Euler's equations; Uniform Rotation; Free Rotation of a Symmetric Top in Space and Body-fixed Frames
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