KUK - LMS

Syllabus

MODULE NO / UNIT	COURSE SYLLABUS CONTENTS OF MODULE	NOTES
Course Code: PHY 102 Course Name: Classical Mechanics
1	Lagrangian and Hamiltonian formulation (12 hrs.) Mechanics of a system of particles, Constraints of motion, Generalized coordinates, D’Alembert’s Principle and Lagrange’s Equations, Simple applications of Lagrangian formulation, Hamilton’s Principle, Lagrange’s equations from Hamilton’s Principle. Extending Hamilton’s Principle to systems with constraints, Advantages of variational principle formulation, Legendre Transformation and Hamilton’s Equations of Motion, Cyclic Coordinates, Routh’s Procedure, Conservation theorems using Hamiltonian, Simple applications of Hamiltonian formulation.
2	Canonical Transformation and Small Oscillations (12 hrs.) Equations of Canonical Transformation and Generating Functions, Examples of canonical Transformations, Poisson bracket and its properties, Angular momenta and Poisson bracket, Jacobi identity, Invariance of Poisson Bracket using Canonical Transformation, Lagrange bracket and its properties, Relation between Poisson and Lagrange brackets, Formulation of the problem under small oscillations, Eigenvalue equation and the principle axis transformation, Frequencies of free vibrations and Normal coordinates, Free vibrations of a linear triatomic molecule.
3	Central Force problem and Hamilton-Jacobi theory (14 hrs.) Reduction to equivalent one body problem, Equations of motion and first integrals, Classification of Orbits, Virial theorem, Differential equation for the orbit and integrable power law Potentials, The Kepler Problem, Deduction of Kepler’s laws, Scattering in Central Force Field, Hamilton-Jacobi Equation for Hamilton’s Principle Function, Harmonic Oscillator Problem as an example of Hamilton-Jacobi Method, Hamilton-Jacobi Equation for Hamilton’s Characteristic Function, Separation of variables in Hamilton-Jacobi Equation, Action Angle Variables, Kepler Problem using Hamilton-Jacobi Equation.
4	Introductory Nonlinear Dynamics (12 hrs.) Classical Chaos: Linear and nonlinear systems, periodic motion, Perturbation and KAM theorem, dynamics in phase space, phase portraits for conservative systems, attractors, classification and stability of equilibrium points, stability analysis of cubic anharmonic oscillator and undamped pendulum, chaotic trajectories and Liapunov exponent, Poincare Map, Henon-Hiels Hamiltonian, bifurcation, driven-damped harmonic oscillator, the logistic equation, Fractals and dimensionality.