Review of Newtonian Mechanics: Newton’s laws of motion, Frames of reference, The Equation of motion for a particle, Conservation theorems, Energy: Stable and Unstable equilibrium, Neutral equilibrium, Potential energy curve. Limitations of Newtonian mechanics.

Calculus of Variations: Statement of the Problem, Euler’s Equation, The “second form of the Euler equation”, Functions with several dependent variables, Euler equation with auxiliary conditions, The d Notation, Hamilton’s Principle.

Lagrangian Dynamics: Need for Lagrangian and Hamiltonian dynamics, generalized coordinates, Constraints and types of constraints, D’Alembert’s Principle, Lagrange’s equation of motion and its application. Derivation of Lagrange’s equation of motion from Hamilton’s Principle, Conservation theorems, Non-Conservative systems and Generalized Potential, Lagrange’s equation with undetermined Multipliers.

Hamiltonian Dynamics: Hamiltonian of a dynamical system, Hamilton’s Canonical equations, Integrals of Hamilton’s equations, Hamilton’s equation from the variation principle.

Canonical Transformations: Legendre Transformation, Examples of canonical transformations, Lagrange and Poisson Brackets, Phase Space and Liouville’s theorem, Virial theorem.

Hamilton Jacobi Theory: Hamilton Jacobi Equation for Hamilton’s principle function, Examples, Action angle variables, Hamilton’s Jacobi theory and its applications.

Central Force Motion: Reduced mass, Conservation theorems, First integral of the Motion, Equation of Motion, Orbits in a central field, Centrifugal Energy and Effective Potential, Planetary Motion – Kepler’s Laws, Orbital Dynamics, Laboratory and Center of Mass Systems, Rutherford Scattering.

Dynamics of Rigid Bodies: Orthogonal Transformations, Inertia Tensor and Dyadics, Angular Momentum, Eulerian Angles, Euler’s Theorem - The Coriolis Force, Euler’s Equations for Forced and Force Free Motion of a Rigid Body, Force Free Motion of a Symmetric Top.

Theory of Small Oscillations: Introduction to Oscillatory Motion, Simple Harmonic Oscillator, Harmonic Oscillations in two-dimensions, Phase Diagrams. General Case of Coupled Oscillations, Eigenvectors and Eigenfunctions, Normal Coordinates, Small Oscillations of Particles on String.

Nonlinear Oscillations and Chaos: Introduction to Chaos, Nonlinear Oscillations, Phase Diagrams for Nonlinear Systems, Plane Pendulum, Jumps, Hysteresis and Phase Lags, Chaos in a Pendulum, Mapping, Chaos Identification.

Recommended Text:
1. Sankara Rao, “Classical Mechanics”, Prentice Hall Inc. India (2005).
2. Jerry B. Marion, Stephen T. Thornton; “Classical Dynamics of Particles and Systems”, 4th edition, Publishers Harcourt Brace and Company (1995).
3. Tai. L. Chow; “Classical Mechanics”, Publisher John Wiley & Sons, Inc. (1995)
4. N.C. Rana, P.S Joag, “Classical Mechanics”, Tata McGraw Hill India (2004).
5. Atam P. Arya; “Introduction to Classical Mechanics”, Allyn and Bacon (1990 )
6. H. Goldstein; “Classical Mechanics”, 2nd Edition, Addison Wesley, Reading, Massachusetts (1980).
7. R.A. Matzner & L. C. Shepley; “Classical Mechanics”, Prentice Hall Inc., London (1991).