MAJOR-IV:PHYS4013: Classical Mechanics and Special Theory of Relativity
(Credits: Theory-05, Practicals-00)
F.M. = 75 (Theory-60, Practical–00, Internal Assessment–15)
Course Objectives: This course covers the Lagrangian and the Hamiltonian formulation of mechanics in systems with constraints, rigid body dynamics, Generating functions for canonical transformations, invariants. The course also covers the Special theory of relativity.
Constraints and their classifications with examples, Inconvenience of Newtonian formulation in practice, The principle of virtual work, D′ Alambert’s principle, Generalized coordinates and momenta, Lagrangian function, Lagrange’s equations of motion, Advantages of Lagrangian formulation over Newtonian one, Cyclic Coordinates, Hamilton’s variational principle, Applications of Lagrangian formulation to simple systems.
Hamiltonian function and its physical significance, Hamilton's canonical equations of motion, Advantages of Hamiton’s formalism over the Lagrangian formulation, Conservation of Energy, Applications of Hamilton’s equations to simple systems, Poisson brackets, Canonical transformations, Generating functions.
[Internal Assessment Solution 2025]
Generalized coordinates of rigid body, body and space reference systems, Angular momentum and moment of inertia tensor of simple rigid body (cube, sphere, cylinder), Principle axes and principle moments of inertia, Kinetic energy of a rigid body, Euler equations of motion of rigid body.
Special Theory of Relativity
Unit 1 Michelson-Morley experiment and its outcome, Two events in two different inertial frames and its correspondence, Simultaneity and order of events, Postulates of special theory of relativity, Lorentz transformations, Lorentz contraction, Time dilation, Twin paradox, Proper time and Proper length Relativistic transformation of velocity and frequency, Time like, space like and light like intervals, Causality. [Home Work-22-June-2025]
Unit 2 Addition of velocities and Lorentz transformations, Variation of mass with velocity, Massless particles and Mass-energy equivalence.
Unit 3 Four vector formalism, Minkowski diagram, The four velocity, Four acceleration, Four force/four momentum, Conservation of four momentum, Energy conservation.
Unit 4 Relativistic Doppler effect, Longitudinal and transverse Doppler effect and aberration, Decay processes.
Unit 5 Transformation of E and B fields, Invariance of Maxwell equations.