Advanced Classical Dynamics

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Lectures

  • Lecture 1. [Non-autonomous Systems]
  • Lecture 2. [Conservative & Dissipative Systems]
  • Lecture 3. [Flow and Bifurcations in 1D]
  • Lecture 4. [Linear Stability Analysis]
  • Lecture 4. [2D Flow & Fixed Points]
  • Lecture 5. [1D Map & Period-2 Orbit]

Numerical Problems

Remarks

  1. Watch Balki's detailed Lectures on Nonlinear Dynamics.

Topics

  • Fluid Dynamics: Different types of derivatives; Equation of continuity and equation of motion for an ideal fluid; Bernoulli’s theorem; Concept of streamlines and vortex lines; Gravity waves and shallow waves; Non-ideal fluids and Navier-Stokes equation.
  • Nonlinear Dynamics: Dynamical systems, Idea of Autonomous and non-autonomous system through examples: free, forced and damped oscillators. Idea of fixed points in one dimensional problem. Flows. Linear stability analysis. Classification of fixed points in 1-D and 2-D through simple examples. x-p phase diagrams, with physical examples for simple 1-D potentials.
  • Special theory of relativit:
    1. Lorentz transformations; vectors and tensors in Minkowski space-time, Transformation properties, Metric tensor, Raising and lowering of indices, Contraction, Symmetric and antisymmetric tensors; 4-velocity and 4-momentum;
    2. Covariant equations of motion; Relativistic kinematics (1 → 2 decay, elastic scattering and Mandelstam variables, inelastic scattering and threshold energy); Lagrangian of a free relativistic particle.

Study Materials

  1. Fluid Dynamics:
    • Feynman Lectures in Physics (Vol.2).
    • Fluid Mechanics (Vol.6) & Theory of Elasticity (Vol.7) - L.D. Landau & E.M. Lifshitz.
    • The Finite Volume Method in Computational Fluid Dynamics - F. Moukalled, L. Mangani & M. Darwish.
  2. Nonlinear Dynamics:
    • Nonlinear Dynamics and Chaos - Strogatz.
    • Introduction to Dynamics - Perceival & Richards.
    • Classical Dynamics - Jose & Saletan.
    • An Introduction to Dynamical Systems and Chaos - Layek.
    • Chaos: An Introduction to Dynamical Systems - Alligood Sauer Yorke.
    • Chaos & Integrability in Nonlinear Dynamics - Tabor.
    • Introduction to Chaos: Physics and Mathematics of Chaotic phenomena - Nagashima & Baba.
  3. Poincarian Relativity:
    • Classical Electrodynamics - J.D. Jackson.
    • Classical Theory of Fields (Vol II) - Landau and Lifshitz.
    • Tensor Analysis - Barry Spain.
    • Mathematical Physics - Arfken-Weber/Murray Spiegel/S.D.Joglekar.