Welcome to Classical Mechanics (PHYS 705) course page
Fall 2024, George Mason University, Physics and Astronomy
[Aug 26, 2024 - Dec 18, 2024]
Fall 2024, George Mason University, Physics and Astronomy
[Aug 26, 2024 - Dec 18, 2024]
Planetary Hall 220
Monday at 16:30-19:10
Prof. Dr. Erdal Yiğit
Primary Textbooks: (1) Classical Mechanics by Goldstein, Poole, Safko, 3rd edition.
Supporting texts: (1) Analytical Mechanics, Hand and Finch, Cambridge University Press. (2) A History of Mechanics, R. Dugas, Dover Books on Physics, (3) A Student's Guide to Lagrangians and Hamiltonians, P. Hamill, Cambridge, (4) Differential Equations, Dynamical Systems, and an Introduction to Chaos, E. India., AP. (5) Classical Mechanics in Geophysical Fluid Dynamics, O. Morita, CRC Press.
Errata page for Goldstein et al.
Homework assignments are based on the problems in the book by Goldstein et al., unless otherwise stated. Chapter numbers refer to the chapters in Goldstein et al.
HWs
Review of Mechanics:
Show that the kinetic energy is given by Eqn 1 in plane polar coordinates.
Chpt 1, problems 1, 2, and 3.
[26 Aug; due: 9 Sept ]
Lagrange equations - I
Chpt 1, problems 7, 8, 9, and 10
[9 Sept; due: 16 Sept ]
Lagrange equations - II & Hamilton's principle
Chpt 1, problems 20, 22, 23, and Chpt 2, problem 1
[16 Sept; due: 23 Sept ]
Hamilton's principle & Calculus of variations
Chpt 2, problems 12 and 14
[23 Sept; due: 30 Sept ]
Central force problem
Chpt 2, problems 20
[30 Sept; due: 7 Oct ]
Kepler problem
Chpt 3, problem 13
[7 Oct; due: 21 Oct ]
Hamilton's equations
Chpt 8, problems 16
A pendulum consists of a mass m suspended by a massless spring with unextended length b and spring constant k.
(a) Sketch the problem.
(b) Use the Lagrangian method to find the equation of motion.
(c) Determine the Hamiltonian and Hamilton's equation of motion.
[21 Oct; due: 28 Oct ]
Canonical transformations
Chpt 9, problem 8
[28 Oct; due: 18 Nov ]
Hamilton- Jacobi Equation & Hamilton Principal Function
Chpt 10, problem 5
[18 Nov; due: 25 Nov]
Oscillations
Obtain the normal modes of vibration for the double pendulum shown in Figure 1.4 in Goldstein, assuming equal lengths, but not equal masses. Show that when the lower mass is small compared to the upper one, the two resonant frequencies are almost equal. If the pendula are set in motion by pulling the upper mass slightly away from the vertical and then releasing it, show that subsequent motion is such that at regular intervals one pendulum is at rest while the other has its maximum amplitude. This is the familiar phenomenon of beats.
[25 Nov; due: 2 Dec]
HW1: Chpt 1, problem 3
(Lecture notes are being continuously updated.)
Syllabus will be updated soon.