National University of Sciences and Technology
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PHY-801 Classical Mechanics
Campus SNS
Programs PG
Session Fall Semester 2016
Course Title Classical Mechanics
Course Code PHY-801
Credit Hours 3-0
Course Objectives Objectives:
 The aim of this course is to provide a solid understanding of the fundamental aspects of classical mechanics. These aspects of classical mechanics endowed with a concrete background in understanding the contemporary fields such as Special Relativity, General Relativity and Quantum Mechanics etc.

 On successful completion of this course, students will be able to
  1. Develop the Lagrangian and Hamiltonian for the system under study.
  2. Obtain the equations of motion.
  3. Solve the equations of motion for different cases.
  4. Apply the concepts of canonical transformations and Poisson brackets.
  5. Treat rigid body rotations from the stand point of matrix transformations.
  6. Applying Hamilton’s Jacobi techniques to solve the motion of mechanical systems.
Detail Content Review of Newtonian Mechanics: Introduction to Mechanics, Newton's Law, Frame of Reference, The equation of motion for a single particle with examples, Limitations of Newtonian Mechanics.Mechanics of system of particles, Constraints, D'Alembert's principle of virtual work and the Lagrange equationApplication of Lagrangian formulation such as Lagrangian for a charged particle in an electromagnetic field, calculation of equation of motion for a single particle using (i) Cartesian coordinates (ii) plane polar coordinates, Atwood's machine, Time dependent constraint-bead sliding on a rotating wire.

Variational principles and Lagrange's equations: Calculation of variations and Hamilton's principle, Derivation of Lagrange's equation from Hamilton's principle, Lagrange multipliers and force of constraint.

Conservation theorems and symmetry properties, Hamiltonian and conservation of energy.The central force problem: Central forces by Lagrangian, the virial theorem, The differential equation for the orbit and integrable power law potentials.Conditions for closed orbits (Bertrand's theorem), Kepler's problem: Inverse square law of force, the motion in time in the Kepler problem, The Laplace-Runge-Lenz vector.Scattering in a central field, Transformation of the scattering problem to laboratory coordinates, The three body problem.

The kinematics of rigid body motion: independent coordinates of a rigid body, Orthogonal transformations, Formal properties of the transformation, The Euler angles and Euler's theorem for finite and infinitesimal rotations.

Rate of change of a vector, The Coriolis effect. The rigid body equations of  motion: Angular momentum and kinetic energy of motion about a point, Review of tensors.The inertia tensor, its eigenvalues and the principal axis transformation, Use of Euler's equation in solving the rigid body problem, torque-free motion of a rigid body and its applications, Precession of orbits.Oscillations: Introduction, Simple harmonic oscillator, The eigenvalue equation and the principal axis transformation, Frequencies of free vibrations and normal coordinates, General problems of coupled oscillationsThe Hamilton equations of motion: Legendre transformations and Hamilton equations of motion, Cyclic coordinates and conservation theorem, Derivation of Hamilton's equation from a variational principle, The principle of least action.Canonical transformations: The equations of canonical transformation and examples, Poisson bracket and criteria for a canonical transformation, Infinitesimal canonical transformation and conservation theorem, Liouville's theorem.Hamilton-Jacobi theory and action-angle variables: The Hamilton-Jacobi equation and its explicit form for Hamilton's characteristic function, Separation of variables in the Hamilton-Jacobi equation, Ignorable coordinates, Statement of Noether’s theorem. Action angle variables.    
Text/Ref Books Main Texts:
  1. Classical Mechanics, by H. Goldstein, C.P. Poole and J.L. Safko, Addison-Wesley 2002
Reference books:
  1. Classical Dynamics of Particles and System, by J.B. Marion and S.T. Thornton, Harcourt Brace College 2003
Time Schedule Fall Semester 2014
Faculty/Resource Person Dr. Faheem Amin
PhD, Physics(Phiilipps, Germany)

Discipline: Nanotechnology