
B.S. CLASSICAL MECHANICS [PHYS521] SYLLABUS

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, NonConservative
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 twodimensions,
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).



