Physics 361, Fall 2010
1
Physics 361/Engineering 361
Analytical Mechanics
Fall, 2010 at Hope College
Instructor: Steve Remillard
Office: VanderWerf 225
Phone: 395-7507
Email: remillard@hope.edu
Office Hours (tentative): M 3:00-3:50; W 9:30-10:20; F 11:00-11:50; (or any other time)
Lecture: M,W,Th&F at 2:00
Please avoid me: M&F 12:00-1:00; W 11:00-12:00; Th 1:00-2:00
My Philosophy for this Course
Unlike the introductory General Physics I, which established the ideas of dynamics, this course has
two objectives: (1) to help you to develop a theoretical grasp of dynamics which then allows you to
solve new problems unaided by examples; and (2) to introduce you to the use of dynamic analysis at
the professional level. We will work through the textbook, Classical Dynamics of Particles and
Systems, by Thornton & Marion, which provides a rigorous development of dynamics. Computer
solutions using Maple will lend a more professional approach to analyzing problems which takes
you beyond simply solving problems.
Text
Classical Dynamics of Particles and Systems, 5th Edition, by Thornton and Marion (ThomsonBrooks/Cole, 2004), ISBN 0-534-40896-6
Student Solutions Manual for Thornton/Marion's Classical Dynamics of Particles and Systems, 5th
Edition (Thomson-Brooks/Cole, 2004), ISBN 0-534-40897-4
Other Recommended Books
• Mechanics, 3rd Edition, by Keith R. Symon (Addison-Wesley, 1971), ISBN 0-201-07392-7
• A Review of Undergraduate Physics, by Bayman and Hamermesh (Wiley, 1986), ISBN 0-47181684-1
• Classical Mechanics, by John R. Taylor (University Science Books, 2005), ISBN 1-891-38922-X
Prerequisites
Phys 280 Introduction to Mathematical Physics and Engineering
Math 232 Multivariable Mathematics II
Course Evaluation
Tests 1, 2 and 3
One cumulative final exam
Homework
60%
20%
20%
(20% each)
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Physics 361, Fall 2010
2
Grading System
The following scale will be used for the cumulative course grade: 93-100%=A, 90-93%=A–, 8790%=B+, 83-87%=B, 80-83%=B–, 77-80%=C+, 73-77%=C, 70-73%=C–, 67-70%=D+,
60-67%=D, Below 60%=F. (Answer to FAQ: 83.0000% is a B, NOT a B-)
The Course Web Site:
http://www.hope.edu/academic/physics/faculty/remillard/PHYS361.html or just go to my
faculty web page found on the physics department web site and select “Teaching”. The
homework assignments will be posted on this website, and there is a password protected page
where you will find solution keys.
Homework – Six very important things you need to know.
o There will be one weekly problem set due in class, usually on Friday. To
accommodate holidays and tests, some problem sets may be due on a different day
than Friday. Consult the assignments page on the course web site.
o The readings listed in the syllabus need to be finished prior to the indicated class date.
This is the only way this course will work for you. Class time will build on the
reading – not replace it. Pop quizzes, which will count as homework points, might
be necessary to force this practice.
o You might need to spend some time outside of class using the facilities in the
advanced lab.
o Unless requested by me or by the problem statement, solutions done with MAPLE or
any other program will be returned ungraded. Evidence that a computer program
was used, such as obvious skipped steps or gobblygook that doesn’t even make sense
to you, might have the same outcome.
o Late policy: 20% per day beginning at 5:00 pm. Weekends included.
Tests & Exam
Three closed book tests will be given. The final exam, which will be cumulative, will be 24 hour
take-home. If you miss a test, you must make it up quickly. You must have informed me prior to
the test time of your situation, and the excuse needs to be a good one.
Disabilities
If you require accommodation for any kind of disability that falls within ADA guidelines please
contact me during the first week of the semester. Several useful services are also available from
Student Development (395-7800) and the Academic Support Center (395-7830).
Comments about email
Please use your firstname.lastname@hope.edu email to communicate with your Hope faculty.
Check your email daily for announcements. You are responsible for any announcement sent out by
me to the class. Also, I would like to encourage you to always use face-to-face communication to
provide feedback to your professors rather than email, as email “venting” so often results in
regrettable one-way miscommunications.
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Physics 361, Fall 2010
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Withdrawing
The deadline for withdrawing from this course or converting to P/F is Nov 5, 2010.
Some Tempting Opportunities for Academic Dishonesty in this Course:
discussing a test with someone who hasn’t taken it; using a homework website or a solution
manual for assignments; using MAPLE to solve homework problems that you are supposed to
solve; copying homework instead of collaborating; Copying off a neighbor during a test or a quiz. I
wasn’t born yesterday and it is very hard to get away with systematic cheating under my watch.
The penalty for cheating on homework or a test can be as severe as an F in the course, and will
certainly result in a report to the provost. Buying a solution manual is the same thing as paying
someone else to do your homework. All work in Physics/Engineering 361 is subject to scrutiny for
plagiarism. See http://www.hope.edu/lib/plagiarism/index.html for more details on Hope College’s
policy on plagiarism and how to avoid plagiarism. Please see the college handbook for the full
college policy on unethical behavior.
Extra Credit Policy
Your grade in this course is determined by your performance on course requirements. You have
enough work to do just to perform well on these course requirements. If that performance is not
going well, adding more work won’t help. Therefore, there is no extra credit in this course.
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Physics 361, Fall 2010
4
Course Schedule
Date
9/1
9/2
9/3
9/6
9/8
9/9
9/10
9/13
9/15
9/16
9/17
9/20
9/22
9/23
9/24
9/27
9/29
9/30
10/1
10/4
10/6
10/7
10/8
10/11
10/13
10/14
10/15
10/18
10/20
10/21
10/22
10/25
10/27
10/28
10/29
11/1
11/3
11/4
11/5
11/8
11/10
11/11
11/12
11/15
11/17
Thornton &
Marion Reading1
1.1-1.2, 2.1
2.2-2.4a
2.4b, Appendix H
1.17, 2.5
2.6-2.7
Appendix A
2.5
3.1-3.2
3.3-3.4
3.5
3.6-3.7
4.1-4.2
4.3-4.4
5.1
Ch. 2-4
6.1-6.2
6.3
6.3
6.6-6.7
7.1-7.2
Optional Symon Topic
Reading2
1.3, 7.3-7.4a
7.4b
7.5
7.8-7.9
7.10-7.11
8.1-8.3
9.1
9.2-9.3
9.4-9.5
9.6
9.10
8.4
8.5-8.6
8.7
8.8
9.1-9.2
9.1-9.3
3.13
3.14
3.15
2.2-2.3
2.4, 2.8, 3.11
2.5
2.5
2.7-2.8
3.9-3.10
2.9
2.10
5.5a
4.1
Ch. 6-8
9.4
9.5
9.6-9.7
9.8
9.9-9.10
9.11
1.15, 10.1-10.2
10.3
1.4-1.14
Introduction; Equations of motion, Part 1
Equations of motion, Part 2
Equations of motion, Part 3
Conservative and non-conservative forces
Energy
Stability
Angular momentum
The simple harmonic oscillator
2D harmonic vibrations; Phase space
Damped vibrations
Driven vibrations
Nonlinear vibrations
Nonlinear phase diagrams; Large angle pendulum
Gravitation and inverse square law forces
Test 1
Introduction to variational calculus
Extreme value problems
The Euler equation
Undetermined multipliers
Hamilton’s Principle
Critical Issues Symposium – no class
Generalized coordinates and Lagrange’s Equations
Lagrangian mechanics
Lagrangian mechanics: systems subject to constraint
Lagrangian mechanics: conservation theorems
Hamiltonian dynamics
Conservation theorems in a central force
Fall Recess
Equations of motion in a central field
Orbits in a central field
Kepler’s laws
Satellite orbital dynamics
Center of mass
Linear momentum
Test 2
No Class
4.2
4.3-4.4
4.6-4.7
4.6
3.16, 4.8
4.5
7.2
7.2
Angular momentum and its conservation
Energy of a system
Elastic collisions (Symon is recommended)
Inelastic collisions
Scattering cross-section; Rutherford scattering
Rocket propulsion
Rotating coordinate systems
Fictitious forces
Vector transformations
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Physics 361, Fall 2010
Date
Thornton &
Marion Reading
11.1-11.2
11.3
11/18
11/19
11/22
11/24
11/25
11/26
11/29
12/1
12/2
12/3
12/6
12/8
12/9
12/10
12/15
5
Optional Symon Topic
Reading
10.1-10.5
Ch. 9-11.3
11.4
11.5
11.6-11.7
11.8-11.9
11.10-11.11
12.1-12.2
12.3
3:00 pm
11.1-11.2
10.5
10.5
11.4
11.5
4.10
4.10
Planar motion
The inertia tensor
Class’s Discretion
Test 3 (May be taken on 11/23)
Thanksgiving – no class
Thanksgiving – no class
Angular momentum of a rigid body
Principal axes of inertia
Moments of inertia and the inertia tensor
Euler Angles
The precessing top
Introduction to coupled oscillations
Two-coupled harmonic vibrations
Class’s discretion
Final Exam
1
The assigned reading is from Thornton and Marion.
2
“Optional reading” does not mean “alternate reading” (except for Nov. 5).
Three copies of Symon are on reserve in the library. You can check them out for 24 hours.
Rev 2