KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS
DEPARTMENT OF PHYSICS
PHYS 301- Classical Mechanics I
TERM 141
Instructor
Bldg. / Office
Phone #
Office Hours
Email
Webpage
: Dr. Abdelkrim Mekki
: 6 - 219
: 860 - 4292
: UTR (11:00AM-12:00AM) or by appointment.
: akmekki@kfupm.edu.sa
: http://faculty.kfupm.edu.sa/phys/akmekki
Course Description:
Topics covered include: Newton's laws of (2) motion and conservation theorems (2), oscillations (3); non-linear
oscillations and chaos (4); Computational study of forced oscillatory motion and nonlinear motion (4); gravitation
(5); Hamilton's variational principle- Lagrangian and Hamiltonian Dynamics (6, 7); Central force (8); Motion in a
non-inertial reference frame (10).
Prerequisite: MATH 202, PHYS 101
Textbook: Thornton S. T. and Marion, J. B.: Classical Dynamics of Particles and Systems, 5th edition, Saunders
College Publishing, 2004.
References:
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Goldstein H, Poole C, and Safko J, “Classical Mechanics”, Addison Wesley 3 rd, edition 2002.
Jose J and Saletan E, “Classical Dynamics: A Contemporary Approach”, Cambridge University Press
(August 13, 1998)
Symon K R: " Mechanics " , Addison-Wesley, 3rd Edition, 1977.
Arya A, “Introduction to Classical Mechanics”, Allyn and Bacon, 1990.
Fowles G. R., and Cassiday G. L.: “Analytical Mechanics”, 6th edition, Saunders College Publishing, 1999.
Zimmerman R. L., and Olness F. I.: “MATHEMATICA for Physics”, Addison-Wesley Publishing
Company, 1995.
Grading:
Homework:
Quizzes
Major exam1
Major exam2
Project
Final Exam
10%
20%
15%
15%
10%
30 %
Homework:
Every chapter you will be given some problems to be solved and returned back the week following the end of that
chapter. There will be few problems that you may need to solve them numerically using MATHEMATICA.
Quizzes:
There will be a quiz at the end of every chapter.
Project:
The project will be on chapter 4. It will be due at the end of the term.
Week
1
2
3
4
5
6
Date
31 Aug. 14
02 Sept.
04
07
09
11
14
16
18
21
23
25 Sept.
12 Oct.
14
16
19
21
23
Topics
Chapter
General Introduction to the course
Newton’s Laws, The Equation of motion of a particle
The Equation of motion of particle (Examples )
The Equation of motion of particle (Examples )
Conservation Theorems
Energy – Chapter 2 Tutorial
2
2
2
2
2
11 Sept. - Last day for dropping course(s) without permanent record
Harmonic Oscillator in 1D
3
Harmonic Oscillator in 2D
3
Phase Diagrams, Damped Oscillations
3
Sinusoidal driving force – Physical systems
3
National Day - Holiday
Chapter 3 Tutorial
Nonlinear Oscillations, Phase Diagrams
Plane Pendulum, Jumps, Hysteresis, Phase Lags, and Chaos in a Pendulum
Mapping, Chaos Identification
Chapter 4 Tutorial
Gravitational Potential
Lines of force and Equipotential Surfaces, Potential concept
Sec
2.1, 2.2
2.3, 2.4
2.4
2.5
2.6
3.1, 3.2
3.3
3.4, 3.5
3.6, 3.7
4
4
4
4.1- 4.3
4.4 - 4.6
4.7, 4.8
5
5
5.1, 5.2
5.3, 5.4
5
5.5
6
6.1, 6.2
Euler’s Equation
Second Form of Euler Equation, Functions with several Variables
Auxiliary Conditions , The Delta Notation
Chapter 6 Tutorial
Review
Hamilton’s Principle
6
6
6
6.3
6.4, 6.5
6.6, 6.7
7
7.1, 7.2
16
18
20
23
25
27
Generalized Coordinates
Lagrange’s Equation of Motion
Undetermined Multipliers
Equivalence of Lagrange and Newton’s Equations
Kinetic Energy
Conservation Theorems Revisited
7
7
7
7
7
7.3
7.4
7.5
7.6
7.7, 7.8
7.9
30
02 Dec.
04
Hamiltonian Dynamics
Dynamical Variables and Variational Calculations
Chapter 7 Tutorial
7
7
7.10
7.11
8
8
8
8.1-8.3
8.4
8.5, 8.6
23 Oct. - Last day for dropping course(s) with grade of "W"
7
26
28
30
Ocean Tides
Chapter 5 Tutorial
Calculus of Variations
27th October 2014 – First Major Exam (Chapters 2-4)
8
9
10
11
12
02 Nov.
04
06
09
11
13
1st December 2014 – Second Major Exam (Chapters 5-7)
13
14
15
16
07
09
11
14
16
18
21
23
25
28
Central Force Motion, Conservations Theorems
Equations of Motion
Orbits in a Central Field, Centrifugal Energy
Chapter 8 Tutorial
Motion in a Non Inertial Frame, Rotating Coordinate Systems
Centrifugal and Coriolis Forces
10
10
18 Dec. - Last day for withdrawal from all courses with grade of "W"
Motion Relative to the Earth
10
Chapter 10 Tutorial
Review1
Review2
10.1, 10.2
10.3
10.4
30 Dec. - 11 Jan. 2015: Final Exam (comprehensive)
Course learning outcomes
On successfully completing the course the students can:
1.
Analyze and apply Newton’s laws that govern the mechanics of a point object in one ant two
dimension problems with an overall average of 55% in exams.
2.
Analyze and apply conservations laws that govern the mechanics of a point object with an overall
average of 55% in exams.
3.
Describe linear oscillatory motion in one and two dimension problems for simple mechanical
systems and analyze problems on damped and forced oscillatory systems with an overall average
of 50% in exams.
4.
Explain the nonlinear oscillations Chaos; explain how the nature of the dynamics is reflected in
the properties of the phase space trajectories; Describe and use numerical method to analyze the
nonlinear dynamics with an overall average of 55% in exam.
5.
Compute and simulate the dynamic behaviour of nonlinear oscillation numerically by using
Mathematica ( or any suitable program such as Matlab, Mathcad, C++ ) software with an overall
average of 60% in total grade.
6.
Calculate and explain problems in the gravitational potential and forces with an overall average of
55% in exam.
7.
Apply Euler’s Equations in some classical problems with an overall average of 60% in exam.
8.
Solve the mechanics problems using Lagrangian formalism, a different method from Newtonian
mechanics with an overall average of 70% in the lab grade.
9.
Solve dynamical problems involving classical particles by using Hamiltonian formulation with an
overall average of 70% in the exam.
10. Describe and solve two bodies system encountered in central forces with an overall average of
70% in the exam.