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Topics in Nonlinear Dynamics

Topics in Nonlinear Dynamics. Instructor: Prof. V. Balakrishnan, Department of Physics, IIT Madras. This is a basic course in classical mechanics at the senior undergraduate/ master's level. It covers the standard topics in this subject, including the Lagrangian and Hamiltonian formalisms. It also places the subject in the broader context of classical dynamical systems.

The phase space description of such systems is highlighted, and the distinction between integrable and chaotic Hamiltonian systems is brought out. The role of symmetries is elucidated, and the connection between symmetry, invariance and conservation principles is explained. Special relativity is also covered, with an emphasis on the invariance and symmetry aspects as applied to classical mechanics. (from nptel.ac.in)

Overview


Lecture 01 - Overview
Lecture 02 - Critical Points of a Dynamical System
Lecture 03 - Two Dimensional Flows
Lecture 04 - Stable and Unstable Manifolds
Lecture 05 - Hamiltonian Dynamics (Part I)
Lecture 06 - Hamiltonian Dynamics (Part II)
Lecture 07 - Hamiltonian Dynamics (Part III)
Lecture 08 - Hamiltonian Dynamics (Part IV)
Lecture 09 - Hamiltonian Dynamics (Part V)
Lecture 10 - Elementary Bifurcations
Lecture 11 - Limit Cycles
Lecture 12 - Poincare Index
Lecture 13 - Illustrative Examples
Lecture 14 - Quiz 1 - Questions and Answers
Lecture 15 - Bead on a Rotating Hoop
Lecture 16 - Types of Dynamical Behaviour
Lecture 17 - Discrete Time Dynamics (Part I)
Lecture 18 - Discrete Time Dynamics (Part II)
Lecture 19 - Discrete Time Dynamics (Part III)
Lecture 20 - Discrete Time Dynamics (Part IV)
Lecture 21 - Coarse-grained Dynamics in Phase Space (Part I)
Lecture 22 - Coarse-grained Dynamics in Phase Space (Part II) and Stochastic Dynamics (Part I)
Lecture 23 - Stochastic Dynamics (Part II)
Lecture 24 - Stochastic Dynamics (Part III)
Lecture 25 - Coarse-grained Dynamics in Phase Space (Part IV) and Stochastic Dynamics (Part IV)
Lecture 26 - Discrete Time Dynamics (Part V)
Lecture 27 - Quiz 2 - Questions and Answers
Lecture 28 - Stochastic Dynamics (Part V)
Lecture 29 - Stochastic Dynamics (Part VI)

References
Topics in Nonlinear Dynamics
Instructor: Prof. V. Balakrishnan, Department of Physics, IIT Madras. This is a basic course in classical mechanics.