Syllabus

Module 1: (4 hours)
Review of Lagrangian formalism and its application, Hamilton’s principle and Hamiltonian mechanics.
Module 2: (14 hours)
The equation of canonical transformation, the sympletic approach to canonical transformation, infinitesimal canonical transformation, Poisson brackets and other canonical invariant, conservation theorem in Poisson bracket formulations, angular momentum Poisson bracket relations. Hamilton-Jacobi theory: Hamilton-Jacobi equation for Hamilton-principle & Hamilton's characteristic functions, separation of variables in H. J. equations, cyclic coordinates, action angle variables for one degree freedom, action angle variables for completely separable systems.
Module 3: (9 hours)
The Kinematics of rigid body motion: Co-ordinates of rigid body, Orthogonal transformation, Properties of transformation matrix, Euler angles, Euler's theorem in motion of rigid body, Infinitesimal rotations, Rate of change of vectors, Coriolis effects.
Module 4: (9 hours)
Rigid body dynamics: Angular momentum & Kinetic energy of motion about a point, inertial tensor and moment of inertia, principal axis transformation and eigenvalue values of inertia tensor, Euler equation of motion, torque free motion of rigid body, heavy symmetrical top with one point fixed, Gyroscope.
Module 5: (5 hours)
Small Oscillations: Formulation, Eigenvalue equation and principal axis transformation, Free vibration and normal coordinates, dissipation and forced vibrations.
Module 6: (7 hours)
Special theory relativity: Basic postulates of special theory of relativity, Lorenz transformation, velocity addition, Relativistic kinematics of collisions and many particle systems, Lagrangian,
Hamiltonian formulations in relativistic mechanics, illustrations (1D harmonic oscillator, hyperbolic motion of particle, motion of a charged particle), Covariant formulation Lagrangian.

To gain an understanding of advanced theories beyond Newtonian mechanics of dynamics of classical systems having full range of speed.

To equip students with effective research skills.

Understanding the concept of Symmetries.

To enhance skills for solving real problems in dynamics using abstract mathematical language.

5. To help students for smooth transition to theories of quantum physics.

At the end of the course, students will be able to learn:
CO1: The fundamentals of Lagrangian and Hamiltonian mechanics and their application in solving problems in classical dynamics.

CO2: The methods like canonical transformation and Poisson brackets to simplify the problem and to find the solutions of a system in phase space. The advanced methods of Hamiltonian-Jacobi and Action-angle variables to find the equation of motion and frequency of periodic motions respectively.

CO3: The kinematics of rigid body and its application to real physical events.
CO4 Dynamics of rigid body with their applications to real problems.
CO5: The formulation of small oscillations of objects which have plenty of applications in other branch of physics.
CO6: Glimpse of advanced special theory of relativity

H. Goldstein, C. P. Poole, and J. Safko, Classical Mechanics, Pearson Education , 3rd Edition.

L. D. Landau and E. M. Lifshitz, Mechanics: Course of Theoretical Physics - Vol. 1, Elsvier , 3rd Edition.

L. Susskind and G. Hrabovsky, Classical Mechanics: The Theoretical Minimum, Penguin Publisher (2014)

K. N. Srinivasa Rao, Classical Mechanics, Universities Press (India) Pvt Ltd.