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Calculus of Variations: Functionals
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Introduction to Classical Mechanics
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- 1 Introduction to Classical Mechanics - Course Introduction
- 2 Classical Mechanics: L1: Introduction. Symmetries of space and time.
- 3 Cassical Mechanics: L2: Generalized coordinates and degrees of freedom
- 4 Classical Mechanics: L3: Virtual Work
- 5 Classical Mechanics: L4: Virtual Work (rigid body)
- 6 Classical Mechanics: L5: d'Alembert Principle
- 7 Classical Mechanics: L6: Euler Lagrange Equation for a holonomic system
- 8 Classical Mechanics: L7: Euler Lagrange Equations. Examples
- 9 Classical Mechanics: L8: Euler Lagrange Equations. Examples continued
- 10 Classical Mechanics: L9: Properties of Lagrangian
- 11 Classical Mechanics: L10: Kinetic term in generalized coordinates
- 12 Classical Mechanics: L11: Cyclic coordinates
- 13 Classical Mechanics: L12: Conservation laws -Conservation of Energy
- 14 Classical Mechanics: L13: Energy Function, Jacobi's Integral
- 15 Classical Mechanics: L14: Momemtum conservation
- 16 Classical Mechanics: L15: Matrices and all that
- 17 Classical Mechanics: L16: Matrices, Forms, and all that
- 18 Classical Mechanics: L17: Principal axis transformation
- 19 Classical Mechanics: L18: Small Oscilaltions
- 20 Classical Mechanics: L19: Oscillations, Normal Coordinates
- 21 Classical Mechanics: L20: Oscillations, Triatomic molecule
- 22 Classical Mechanics: L21: Triatomic molecule normal coordinates
- 23 Classical Mechanics: L22: Coupled pendulums, normal modes
- 24 Classical Mechanics: L23: Coupled pendulums, Beats
- 25 Classical Mechanics: L24: Oscillations, General solution
- 26 Classical Mechanics: L25: Forced oscillations
- 27 Classical Mechanics: L26: Damped oscillations
- 28 Classical Mechanics: L27: Forced Damped oscillations
- 29 Classical Mechanics: L28: one dimensional systems
- 30 Classical Mechanics: L29: Two-body problem
- 31 Classical Mechanics: L30: Two-body problem, Kepler's second law
- 32 Classical Mecahnics: L31: Two-body problem, Kepler problem
- 33 "Classical Mecahnics: L31: Two-body problem, Conic Sections in Polar Coordinates"
- 34 Classical Mechanics: Two-body problem, Ellipse in polar coordinates
- 35 Orbits in Kepler Problem
- 36 Apsidal distances, eccentricity of orbits
- 37 Kepler's Third law; Laplace-Runge-Lenz vector
- 38 Rigid Body, degrees of freedom
- 39 Rigid Body, Transfromation matrix
- 40 Rigid Body, Euler Angles
- 41 Parameterization using Euler Angles
- 42 Rigid Body, Euler's Theorem
- 43 General motion of a rigid body
- 44 Moment of Inertial Tensor
- 45 Principal Moments
- 46 Langrangian of a rigid body
- 47 Motion of a free symmetric top
- 48 Angular velocity using Euler angles
- 49 Lagrangian of a heavy symmetric top
- 50 Classical Mechanics: First integrals of a heavy symmetric top
- 51 Classical Mechanics: Nutation and Precission of a heavy symmetric top
- 52 Sleeping Top
- 53 Rotating Frames. Euler Equations
- 54 Calculus of Variations: Functionals
- 55 Method of Lagrange Multipliers
- 56 Calculus of Variations: Condition for extremum
- 57 Calculus of Variations: Several variables
- 58 Cartesian Tensors
- 59 Hamiltonian Mechanics: Hamilton's equations of motion
- 60 Hamiltonian Mechanics: Liouville's theorem
- 61 Hamiltonian Mechanics: Poisson Bracket
- 62 Hamiltonian Mechanics: Canonical Coordinates
- 63 Hamiltonian Mechanics: Generating Function of Canonical Transformations
- 64 Hamiltonian Mechanics: Generating functions of the 4 kinds
- 65 Examples of Generating Functions
- 66 Harmonic Oscillator (Canonical Transformations)
- 67 Invariance of Poisson Brackets
- 68 Normal modes of triatomic molecule using Mathematica
