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. [2D Flow]
  • Lecture 5. [1D Map]

Numerical Problems

Remarks

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

Topics

  • Nonlinear Dynamics:
    1. Definition of a dynamical system. Casting Newton’s equation for a particle in the dynamical system form. Autonomous and non-autonomous system through examples: free, forced and damped oscillators. Idea of conservative dissipative and anti-dissipative systems. Discussion of Mathieu, Duffing, and van der Pol oscillator in this context.
    2. Idea of fixed points in one dimensional problems. Flows. Linear stability analysis. Classification of fixed points through simple examples: both geometrical and linear stability analysis approach should be emphasized.
    3. Canonical forms and their discussions. Associated phase diagrams. Physical examples.
    4. Two dimensional systems and their analysis from the point of view of linear stability. Periodic obits in the form of center and limit cycles. Their stability. Examples: Lotka Volterra (predator-prey), Duffing and Van der Pol oscillator.
    5. One dimensional maps. Idea of fixed point of a map through iterations. Stability of the fixed point and the cobweb plot. Tent and Bernoulli maps. Their graphical representation. Idea of a period two orbit.

Study Materials

  1. Nonlinear Dynamics and Chaos - Strogatz.
  2. Introduction to Dynamics - Perceival & Richards.
  3. Classical Dynamics - Jose & Saletan.
  4. An Introduction to Dynamical Systems and Chaos - Layek.
  5. Chaos: An Introduction to Dynamical Systems - Alligood Sauer Yorke.
  6. Chaos & Integrability in Nonlinear Dynamics - Tabor.
  7. Introduction to Chaos: Physics and Mathematics of Chaotic phenomena - Nagashima & Baba.