Classical Mechanics: From Newtonian to Lagrangian Formulation

Week 1: Review of basic Newtonian mechanics, kinematics problems, Motion under resistance: terminal velocity, System with variable mass: Rocket, raindrop, etc. 

Week 2: Central forces: plane polar co-ordinate system,2-body central force problem, general equation of the orbit, Kepler’s laws of planetary motion

 Week 3: Effective potential of central force, Escape velocity, eccentricity of the orbit under various initial conditions Satellite, Ballistic missile and orbit transfer 

Week 4: Moving co-ordinate system: pseudo forces, Coriolis and centrifugal force, Foucault’s pendulum, Introduction to system of particles 

Week 5: Dynamics in center of mass frame, introduction to rigid body,Degrees of freedom (DOF) and constrains, Rotational dynamics of rigid body, moments of inertia tensor 

Week 6: Principle moments of inertia, ellipsoid of inertia, parallel and perpendicular axis theorem, Euler’s equation of rigid body rotation under external torque, Torque free motion of spherical, symmetric and asymmetric top 

Week 7: Introduction to Euler angles, pitch, precession and nutation, The heavy symmetric top, the energy equation Special case of ‘fast’ and ‘sleeping’ top 

Week 8: Lagrangian dynamics: Forces of constrain, virtual displacement, Principle of virtual wok and D’Alembert’s principle, Generalized co-ordinates, Lagrange’s equation of 1st kind, Lagrange’s undetermined multiplier 

Week 9: Generalized velocity and force, Lagrange’s equation of 2nd kind, Lagrangian, Classification of constrains, Lagrange’s equations for non-holonomic systems, Dissipation and gauge function, most general form of Lagrange’s equation, review of rigid body including heavy symmetric top 

Week 10: Variation principle, calculus of variation, Principle of least action and Lagrange’s equation from it Application of variation principle (catenary, geodesic,etc.) 

Week 11: Small oscillation: Introduction to coupled systems, normal modes, Types of equilibrium, Kinetic and potential energy of a coupled system, expression of energy in matrix form, Equation of motion of a coupled system, normal frequencies , eigenvalues and eigenvectors of K.E. and P.E. matrices, 

Week 12: Diagonalization of K.E. and P.E. matrices, Normal modes of oscillation, Examples (linear molecules, spring mass systems etc.)