Classical Mechanics-I

ABOUT THE COURSE: This is first course to introduce the concepts of Classical Mechanics which is pre-requisites for more advanced courses like Advanced Classical Mechanics, Quantum Mechanics, Statistical Mechanics, Classical and Quantum field theories. In this we will learn mainly Lagrangian and Hamiltonian formulation in a very simple manner with many examples along with theory of small oscillation and two body central force problem. This will be helpful to students who will be writing national level examinations like NET, GATE etc.INTENDED AUDIENCE: 3rd Year UG students and/or 1st Year PG studentsPREREQUISITES: 1. Mechanics2. Elementary Mathematical Physics (Calculus, Matrices, Vectors)

Week 1:General Introduction, Newton’s Laws of Motion, Degrees of freedom, Constraints, Generalized Coordinates

Week 2:Virtual displacements, principle of virtual work, D’Alembert’s principle, Lagrange equations. Examples
Week 3:Calculus of Variation, Hamiltion’s Principle, Lagrangian, Euler Lagrange’s equation.
Week 4:Properties of Lagrangian, Structure of Lagrangian, Construction of Lagrangian for simple systems.
Week 5:Symmetries and conservational laws, Cyclic coordinates, Virial theorem, Principle of Mechanical Similarities
Week 6:Velocity dependent potentials, Lagrangian for a charged particles in the electromagnetic field, Rayleigh Dissipation function
Week 7:Lagrange’s undetermined multipliers, applications Lagrange’s equation for nonholonomic systems, Examples
Week 8:Legendre transformations and Hamilton’s equations of motion, Hamiltonian for a charge particle in Electromagnetic field, Poisson Brackets.
Week 9:Canonical transformation, Generating functionals, Canonical transformation and Poisson Brackets, Applications
Week 10:Two body central force problem, reduction to the equivalent one body problem, Differential equation for the orbit and integrable power law potential.
Week 11:Condition for stable circular orbit, Kepler problems. Theory of small oscillation, general case of coupled oscillators,
Week 12:Eigen vectors and eigen frequencies, Normal mode and normal coordinates. Vibration of linear CO2 molecule.