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• To learn the discipline-specific knowledge in classical mechanics, which includes

reduction of two body problem to one body problem, central force problem,

planetary motion etc.

• To understand the properties of macroscopic systems using the knowledge of the

properties of individual particles

• To learn the different types of statistical distribution function in order to study the

macro and microscopic behaviors.

Upon successful completion of this course, students will be able to:

• Understand the equation of motion for different system.

• Understanding the different transformations and their applications.

• Know the concepts of classical mechanics and apply these concepts in the area of

science.

**Module-I**

Central force problem: Laboratory and centre of mass frames, Reduction of two-body

problem to one-body problem, Non inertial frames and pseudo forces, Central force and motion

in a plane, Differential equation for an orbit, Kepler’s laws of planetary motion, virial theorem

**Module II**

Lagrangian and Hamiltonial Dynamics: Constraints, D’Alembert’s principle, Lagrange’s

equations from D’Alembert’s principle, generalized coordinates, Hamilton’s equations,

Hamilton’s equations in different coordinate systems, variation principle, Euler-Lagrange’s

equations,

**Module III**

Canonical transformations and Poisson Bracket: Canonical transformations, Legendre

transformations, Generating Functions, Application of canonical transformations, properties of

Poisson brackets, Lagrange brackets, Invariance of Poisson bracket under canonical

transformations, phase space, Invariance and Noether theorem, Liouville’s theorem.

**Module IV**

Hamiltonian-Jacobi Theory and Small Oscillation: Hamiltonian-Jacobi equation, harmonic

oscillator problem, Kepler’s problem, Action and angle variables. General theory of small

oscillations: normal modes, normal coordinates and normal frequencies of two coupled

pendulum, double pendulum and vibrations of linear triatomic molecule.

**Module-V**

Relativistic classical mechanic: Postulates, Special theory of relativity-Lorentz

transformations, relativistic kinematics and mass–energy equivalence, Doppler’s effect of light

**Module-VI**

Classical statistical mechanics:

Phase space, ensembles, and partition functions. Free energy and its connection with

thermodynamic quantities. MB statistics and applications.

**Module-VII**

Quantum statistical mechanics:

BE statistics and FD statistics and their applications, Bose Einstein condensation. first and

second order phase transitions, phase equilibria, critical point. Blackbody radiation and

Planck's distribution law, Ising model.

**Text Book:**

1. Classical Mechanics by J C Upadhyaya, Himalaya Publishing House, 2014.

2. Statistical Mechanics by R.K Pathria, Oxford

**Reference Books:**

1. Classical Mechanics by H Goldstein, Pearson, 3rd Edition, 2011.

2. Classical Mechanics by Landau &Lifshitz, 7th Ed, CBS Publishers, New Delhi, 2010.

3. Differential Equations, Dynamical Systems and an Introduction to Chaos, MW Hirsch, S

Smale, RL Devaney.

Session-1

centre of mass frames

https://www.youtube.com/watch?v=oivxjoHy8s4&list=PLb2lQ33Kj040FSiv2YoiN6W0IfUgQ8Gj_&index=2

Session-2

Reduction of two-body problem to one-body problem

Session-3

Non inertial frames and pseudo forces, Central force and motion

in a plane

Session-4

Differential equation for an orbit, Kepler’s laws of planetary motion, virial theorem

Session-5

Constraints, D’Alembert’s principle, Lagrange’s equations from D’Alembert’s principle

Session-6

generalized coordinates, Hamilton’s equations

Session-7

Hamilton’s equations in different coordinate systems, variation principle

Session-8

Euler-Lagrange’s equations

Session-9

Canonical transformations, Legendre transformations, Generating Functions

Session-10

Application of canonical transformations, properties of Poisson brackets, Lagrange brackets