Topics in Nonlinear Dynamics

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.

Mod-01 Lec-01 Overview.
Mod-01 Lec-02 Critical points of a dynamical system.
Mod-01 Lec-03 Two-dimensional flows.
Mod-01 Lec-04 Stable and unstable manifolds.
Mod-01 Lec-05 Hamiltonian dynamics (Part I).
Mod-01 Lec-06 Hamiltonian dynamics (Part II).
Mod-01 Lec-07 Hamiltonian dynamics (Part III).
Mod-01 Lec-08 Hamiltonian dynamics (Part IV).
Mod-01 Lec-09 Hamiltonian dynamics (Part V).
Mod-01 Lec-10 Elementary bifurcations.
Mod-01 Lec-11 Limit cycles.
Mod-01 Lec-12 Poincar´e index.
Mod-01 Lec-13 Illustrative examples.
Mod-01 Lec-14 Quiz 1. Questions and answers.
Mod-01 Lec-15 Bead on a rotating hoop.
Mod-01 Lec-16 Types of dynamical behaviour.
Mod-01 Lec-17 Discrete time dynamics (Part I).
Mod-01 Lec-18 Discrete time dynamics(Part II).
Mod-01 Lec-19 Discrete time dynamics (Part III).
Mod-01 Lec-20 Discrete time dynamics (Part IV).
Mod-01 Lec-21 Coarse-grained dynamics in phase space (Part I).
Mod-01 Lec-22 Coarse-grained dynamics in phase space (Part II).
Mod-01 Lec-23 Stochastic dynamics (Part II).
Mod-01 Lec-24 Stochastic dynamics (Part III).
Mod-01 Lec-25 Coarse-grained dynamics in phase space (Part IV).
Mod-01 Lec-26 Discrete time dynamics (Part V).
Mod-01 Lec-27 Quiz 2. Questions and answers.
Mod-01 Lec-28 Stochastic dynamics (Part V).
Mod-01 Lec-29 Stochastic dynamics (Part VI).