Course

UNIT 1:Canonical Transformations: Equations of Canonical transformation, Examples-Simple Harmonic Oscilla- tor, Liouvilles Theorem. Volume preservation in phase Space, Generating function, Conditions for canonical transformation and problem.UNIT 2:Poisson Brackets: Definition, Identities, Poisson theorem, Jacobi-Poisson theorem, Jacobi identity, invariance of PB under canonical transformation- Angular momentum Poisson bracket- Symmetry, invariance and Noether’s theorem.UNIT 3:Hamilton- Jacobi Theorem: Hamilton- Jacobi Equation for Hamiltons principal function, Hamilton- Jacobi Equation for Hamiltons Characteristic Function, Harmonic oscillator problem, Actionangle variable in Systems of one variable, Kepler Problem in Action-angle variable.UNIT 4:Small oscillations: Formal theory of small oscillations as Eigenvalue problems, applications to diatomic and triatomic molecules, modes of vibrations.UNIT 5:Introduction to Chaos and Nonlinear Dynamics: Fixed points, Bifurcation, and Limit cycles, Lorenz Equations, The Logistic Map, Fractals, and Strange Attractors.

Pre-requisites: Mechanics, Classical Mechanics 1, Mathematics 1&2Course Objectives: To study, understand and apply principles of Hamiltonian dynamics to solve dynamical systemsCourse outcomes:CO1: Study canonical transformations and apply it to mechanical problemsCO2: Study the properties of Poissons bracket and apply it to dynamical problems CO3: Apply Hamilton Jacobi theory for Harmonic oscillator and Kepler problemCO4: Apply small oscillation theory developed in getting the frequencies of different of modes of oscillations in a coupled systemCO5: Introduction to Chaos and Nonlinear dynamics

TEXT BOOKS:1.H. Goldstein, C. Poole and J. Safko, Classical Mechanics, Pearson Education, 3rd Edition, 2011.2.Landau and Lifshitz, Mechanics, Butterworth-Heinemann, 3rd Edition, 1982.3.S.T. Thornton and J.B. Marion, Classical Dynamics of Particles and Systems, Cengage, 5th edition, 2012.4.Walter Greiner, Classical Mechanics: Systems of Particle and Hamiltonian Dynamics, Springer,2nd Edition, 20095.Lecture Series on Classical Physics by Prof. V. Balakrishnan – https://www.youtube.com/ watch?v=Q6Gw08pwhws&list=PL5E4E56893588CBA86.Steven H Strogatz, Non Linear Dynamics and Chaos, Perseus Books Publishing, 1994.