Classical Mechanics

Instructor : Dr Abdul Hameed Nayyar
Term : Spring 2012
Level : Undergraduate
Course Code : PHY 301
Course Status : Physics Core
Course Outline


Course Description

The course goes beyond the first course PHY 101 Mechanics. After a brief recapitulation of the ways to solve Newton’s equation of motion in a variety of simple problems in mechanics, and looking at the specific problem of accelerating coordinates and inertial forces, it introduces the formalisms of Lagrangian and Hamiltonian Mechanics with applications to a number of physical problems, especially the central force problem. It takes the formalism to canonical transformations, generating functions and Poisson brackets. The course will also ask students to simulate physics problems on computers.


WEEKLY TOPICS, QUIZZES, ASSIGNMENTS, EXAMS

Week Lectures Tentative Topics Quizzes Assignments Exams
1-2 1-4 Introduction to mechanics, conservative forces, conservative theorems, conservative laws for a system of particles. Mechanics of system of particles:
(a) Constraints, generalized coordinates (with an example of double pendulum)
(b) D’Alembert principle
(c) Lagrange’s equation of motion
Quiz 1
Solution
Assignment 1
Solution
3 5-6 Velocity dependent potential, dissipative force, simple application of the Lagrangian formulation Quiz 2
Solution
4 7-8 Calculus of variations. Hamilton’s principle of least action and Lagrange equation of motion Quiz 3
Solution
5-6 9-12 Accelerating coordinates and inertial forces, centrifugal force, Coriolis force. Effect of Coriolis force on earth as rotating frame. Quiz 4
Solution
Assignment 2
Solution
7-8 13-15 Central force problem: Kepler problem and orbital motion; small deviations from circular orbits, conditions for closed orbits. Midterm Exam 1
Solution
9 Midterm break
10-11 16-18 Central force problem: orbital transfer and gravitational boosts, The scattering problem. Quiz 5
Solution
Assignment 3
Solution
12-13 19-22 Hamiltonian mechanics; Hamilton’s equation of motion. Quiz 6
Solution
Quiz 7
Solution
Assignment 4
Solution
14 23-24 Canonical transformation.Generating functions.Poisson brackets. Midterm Exam 2
Solution
15 25-26 Many particle systems: center of mass frame, scattering / Collisions. Motion with a variable mass-Rockets Quiz 8
Solution
17 Final Exam
Solution