Classical Mechanics-I

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.