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.
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