Syllabus#

Course Information#

  • Instructor(s): Michael McNeil Forbes m.forbes+521@wsu.edu

  • Course Assistants:

  • Office: Webster 947F

  • Office Hours: TBD

  • Course Homepage: https://schedules.wsu.edu/List/Pullman/20233/Phys/521/01

  • Class Number: 521

  • Title: Phys 521: Classical Mechanics

  • Credits: 3

  • Recommended Preparation: Undergraduate mechanics and calculus including calculus of variations, Newton’s laws, Kepler’s laws, conservation of momentum, energy, angular momentum, moment of inertia, torque, angular motion, friction, etc.

  • Meeting Time and Location: MWF, 11:10am - 12:00pm, Webster 941, Washington State University (WSU), Pullman, WA

  • Grading: Grade based on assignments and project presentation.

Textbooks and Resources#

Required#

Alexander L. Fetter and John Dirk Walecka: “Theoretical Mechanics of Particles and Continua”, Dover (2003).

This textbook provides a concise and thorough introduction to classical mechanics, including a discussion of fluids and elastic materials that is missing from many other texts. We will only cover roughly the first half of the text in this course, but it is a worthwhile book to have. (Available from Amazon as a Dover Edition.)

Alexander L. Fetter and John Dirk Walecka: “Nonlinear Mechanics: A Supplement to Theoretical Mechanics of Particles and Continua”, Dover (2006).

The supplement provides a complete derivation of the Lorenz equations - the first example of a chaotic system - and presents a derivation of the KAM theorem, demonstrating some modern results in classical mechanics. (Available from Amazon as a Dover Edition.)

L. D. Landau and E. M. Lifshitz: “Mechanics”, Pergamon Press (1969).

Classic textbook. Very concise introduction to the key concepts in classical mechanics, including some topics omitted from other work such as parametric resonances and the adiabatic theorem. (Available online through the WSU Library.)

Additional required readings will be made on Perusall with a forum for discussion.

Additional Resources#

R. Douglas Gregory: “Classical Mechanics”. Cambridge University Press (2006).

Undergraduate textbook. Not very insightful, but provides a good review and contains quite a few problems. (Available online through the WSU Library..)

A. Fasano, S. Marmi, and B. Pelloni: “Analytical Mechanics : An Introduction”. Oxford Graduate Texts (2006).

Texbook at a comparable level to Fetter and Walecka with many problems. For me, the presentation seems a little formal, and the problems seem to interfere with the flow, so I am not sure it is the best book to learn from. It is great, however, for finding problems to test ones understanding. (Available online through the WSU Library..)

O. L. deLange and J. Pierrus: “Solved Problems in Classical Mechanics: Analytical and Numerical Solutions with Comments”. Oxford University Press (2010). (Available online through Library.)

Large collection of problems and solutions including numerical problems. The numerical problems are particularly interest since they go beyond what is typically seen in purely analytic texts. (Available online through the WSU Library..)

G. J. Sussman and J. Wisdom: “Structure and Interpretation of Classical Mechanics”. MIT Press (2015). (Available online through Library.)

Quite a different presentation of the core results from a more formal perspective with many interesting numerical examples. The notation may not be completely familiar - the authors use functional notation and the Scheme programming language. For example, the usual Euler Lagrange equations

\[\begin{gather*} %\newcommand{\diff}[2]{\frac{\mathrm{d}{#1}}{\mathrm{d}{#2}}} %\newcommand{\pdiff}[2]{\frac{\partial{#1}}{\partial{#2}}} \diff{}{t} \pdiff{L}{\dot{q}^i} - \pdiff{L}{q^i} \end{gather*}\]

becomes

\[\begin{gather*} D(\partial_2 L\circ \Gamma[q]) - \partial_1L \circ \Gamma[q] = 0 \\ \Gamma[q] = (t, q(t), Dq(t), \dots). \end{gather*}\]

The ability to be able to recognize and understand results in a slightly different “language” can be extremely valuable for checking one’s understanding and cementing concepts. Thus, while I do not recommend learning from this text, I highly recommend reading it to check that you really understand the concepts. (Available online through the WSU Library..)

Canvas

The course material is hosted on the WSU Canvas system https://canvas.wsu.edu. Check the webpage there for changes to the schedule.

Computation Platform: CoCalc (http://cocalc.com)

This will be used for assignment distribution and for numerical work.

Student Learning Outcomes#

The main objective of this course is to enable students to explain physical phenomena within the realm of classical mechanics, making appropriate simplifying approximations to formulate and solve for the behavior of mechanical systems using mathematical models, and communicating these results to peers.

By the end of this course, the students should be able to take a particular physical system of interest and:

  1. Understand the Physics: Identify the appropriate quantities required to describe the system, making simplifying assumptions where appropriate with a quantitative understanding as to the magnitude of the errors incurred by making these assumptions.

  2. Define the Problem: Formulate a well-defined model describing the dynamics of the system, with confidence that the model is solvable. At this point, one should be able to describe a brute force solution to the problem that would work given sufficient computing resources and precision.

  3. Formulate the Problem: Simplify the mathematical formulation of the problem as much as possible using appropriate theoretical frameworks such as the Lagrangian or Hamiltonian frameworks.

  4. Solve the Problem: Use analytic and numerical techniques to solve the problem at hand.

  5. Assess the Solution: Assess the validity of the solutions by applying physical principles such as conservation laws and dimensional analysis, use physical intuition to make sure quantities are of a reasonable magnitude and sign, and use various limiting cases to check the validity of the obtained solutions.

  6. Communicate and Defend the Solution: Communicate the results with peers, defending the approximations made, the accuracy of the techniques used, and the assessment of the solutions. Demonstrate insight into the nature of the solutions, making appropriate generalizations, and providing intuitive descriptions of the quantitative behavior found from solving the problem.

A further outcome relates to the department requirement for students to demonstrate this proficiency through a series of general examinations, and a more general requirement for the students to interact face-to-face with other physicists.

  1. Proficiency: Be able to demonstrate proficiency with these skills. In particular, be able to rapidly formulate and analyze many classical mechanics problems without external references.

Expectations for Student Effort#

Students are expected to:

  1. Stay up to date with reading assignments as outlined in the [Reading Schedule][reading schedule].

  2. Participate in the online forums, both asking questions and addressing peers questions.

  3. Identify areas of weakness, work with peers to understand difficult concepts, then present remaining areas of difficulty to the instructor for personal attention or for discussion in class.

  4. Complete assignments on time, providing well crafted solutions to the posed problems that demonstrate mastery of the material through the [Learning Outcomes][learning outcomes] 1-6. Final solutions much be written using proper English, including complete sentences with a clear logical progression through all steps of the solution. Excessive verbosity is not required, but the progression through the solution must be clear to the reader, along with a justification of all assumptions and approximations made.

    Submitted solutions should not contain incomplete or random attempts at solving a problem: they should contain a streamline approach proceeding directly and logically from the formulation of the problem to the solution. (Student’s are encouraged to discuss their intended approach with peers and with the instructor well before the deadline in order to obtain the feedback required to formulate a proper solution for submission).

  5. Find or formulate exam problems at a level appropriate for completion of the physics department comprehensive examinations, and practice solving these under exam conditions, seeking help from the instructor as required to develop the required proficiency of the material.

  6. Choose a topic for the final project, and obtain approval from the instructor by November 1.

  7. Complete the final project, and present at the end of semester (typically one evening during the last week of classes, but the final date will chosen by polling everyone’s schedules.

  8. Successfully complete both the midterm and final examinations.

For each hour of lecture equivalent, students should expect to have a minimum of two hours of work outside class.

Assessment and Grading Policy#

The learning outcomes will be assessed as follows:

Assignments:

Throughout the course, students will be expected to demonstrate outcomes 1-6 applied to well-formulated problems demonstrating the techniques currently being taught (see the following [Course Outline]). Successful completion of the assignments will assess the student’s ability with these skills while they have access to external resources such as the textbook, and without stringent time constraints. A peer-grading component of the course will help ensure that written solutions effectively communicate the results as per outcome 6.

Important

In as many assignments as possible, I will provide numerical solutions against which you can check your formula on CoCalc. In order for me to grade your homework, I expect:

  1. Either you get the correct result and your solution matches the numerics.

  2. You make an appointment with me before the assignment is due to discuss what might be going wrong.

If you hand in an assignment with an incorrect solution, and have not contacted me before-hand to discuss what might be going wrong, then you may get zero on the assignment.

If you have difficulty, please first speak with your classmates. If you cannot resolve the issue, then at this point it will be productive for a group to make an appointment with me to discuss.

In Fall 2023, we plan to hold open iSciMath lab/office hours in the Band Room Friday 2-4:30pm. You may stop by these sessions to discuss any issues you have. I am also available for appointment by Zoom.

Exams:

The proficiency of the students to rapidly apply these skills without external resources (outcome 7) will be assessed through time-limited midterm and final examinations. Time-permitting, exams will contain both written and oral portions to simulate our comprehensive exam procedure. The oral portion will help assess the student’s communication skills (outcome 6).

Readings:

Students will be expected to keep up with the reading assignments. This will be assesed by students participating in the class Perusall discussions, with at least 2 annotations per reading assignment, or with a submission in the form of a summary of the reading, the student’s own derivation of a key result, etc. This will assess their ability to communicate about classical mechanics.

Final Project:

The ability of the students to analysis an unstructured mechanics problem in an open-ended context will be assessed through their completion and defense of a final class project in an area of their choosing. This will give the students a chance to exercise their skills in a context much closer to that in which they will encounter while performing physics research.

The final grade will be converted to a letter grade using the following scale:

Percentage P

Grade

90.0% ≤ P

A

85.0% ≤ P < 90.0%

A-

80.0% ≤ P < 85.0%

B+

75.0% ≤ P < 80.0%

B

70.0% ≤ P < 75.0%

B-

65.0% ≤ P < 70.0%

C+

60.0% ≤ P < 65.0%

C

55.0% ≤ P < 60.0%

C-

50.0% ≤ P < 55.0%

D+

40.0% ≤ P < 50.0%

D

P < 40.0%

F

The following table shows how many point you may earn at most from each component of the course:

  • 10: Reading Assignments

  • 40: Homework (or 20 Homework + 20 Project)

  • 25: Midterm Exams:

  • 25: Final Exam

Optional Project#

There will be an optional project in this course which may be used for 25 of the homework points. Further details will be discussed later: you may choose the topic, but must run your proposal by the instructor.

Exams#

The exams will be administered in two parts, similar to how the department qualifying exams are administered. First you will submit a written portion. You will then schedule an oral exam with instructor during which you will be asked questions about your written work, and given an opportunity to explain your reasoning. If you do not feel that the instructor has arrived at an accurate assessment of your exam performance after the oral portion, you may opt to have your written exam graded in detail and will receive that as your grade (with the exception being if it is discovered during the oral portion that your written portion is not your work). However, our experience is that the oral portion generally improves ones grade.

The final exam is scheduled for Tuesday 12 December 2023 at 10:30am.

Attendance and Make-up Policy#

While there is no strict attendance policy, students are expected attend an participate in classroom activities and discussion. Students who miss class are expected to cover the missed material on their own, e.g. by borrowing their classmates notes, reviewing recorded lectures (if available), etc.

Course Timeline#

The following details the content of the course. It essentially follows the main textbook. Content from the supplement will be inserted as appropriate throughout. Details and further resources will be included on the lecture pages on the Canvas server.

Course Outline#

  1. Introduction and Basic Principles (~1 week)

    • Why study classical mechanics?

    • Newtonian mechanics.

    • Symmetry and Conservation.

    • Central Forces

    • Kepler

    • Scattering

  2. Accelerated Coordinate Systems (~1 week)

    • Change of coordinates

    • Centripetal acceleration

    • Coriolis effect

  3. Lagrangian Dynamics (~2 weeks)

    • Why another formulation?

    • Constraints

    • Euler-Lagrange Equations

    • Calculus of Variations

    • Hamilton’s Principle

    • Generalized momenta

    • The Path Integral approach to Quantum Mechanics

  4. Small Oscillations (~1 week)

    • Normal modes

    • Linear Equations

    • Stability

  5. Rigid Bodies (~1 week)

    • Moment of Inertia

    • Euler’s Equations

  6. Hamilton Dynamics (~2 weeks)

    • Canonical Transformations

    • Hamilton-Jacobi Theory

    • Action-Angle Variables

    • The Canonical Quantization approach to Quantum Mechanics

  7. Strings, Waves, and Drums (~1 week)

    • Lagrangian for continuous systems

    • Boundary conditions

    • Numerical solutions of the wave equation

  8. Non-linear Mechanics (SIII: Discrete Dynamical Systems) (~2 weeks)

    These topics will be introduced as we progress through the course, inserted into the appropriate locations.

  9. Canonical Perturbation Theory (~2 weeks)

    These topics will be introduced as we progress through the course, inserted into the appropriate locations.

  10. Special topics and review.

    • How these topics will be covered depends on interest. One option is to discuss superfluidity with some numerical examples demonstrating vortices, vortex dynamics, and related phenomena.

    • Duffing Oscillator

    • Stability Analysis

    • Chaos

    • Fluids

    • Special Relativity

Other Information#

Policy for the Use of Large Language Models (LLMs) or Generative AI in Physics Courses#

The use of LLMs or Generative AI such as Chat-GPT is becoming prevalent, both in education and in industry. As such, we believe that it is important for students to recognize the capabilities and inherent limitations of these tools, and use them appropriately.

To this end, please submit 4 examples of your own devising:

  • Two of which demonstrate the phenomena of “hallucination” – Attempt to use the tool to learn something you know to be true, and catch it making plausible sounding falsehoods.

  • Two of which demonstrate something useful (often the end of a process of debugging and correcting the AI).

Note: one can find plenty of examples online of both cases. Use these to better understand the capabilities and limitations of the AIs, but for your submission, please find your own example using things you know to be true. If you are in multiple courses, you may submit the same four examples for each class, but are encouraged to tailor your examples to the course.

Being able to independently establish the veracity of information returned by a search, an AI, or indeed any publication, is a critical skill for a scientist. If you are the type of employee who can use tools like ChatGPT to write prose, code etc., but not accurately validate the results, then you are exactly the type of employee that AI will be able to replace.

Any use of Generative AI or similar tools for submitted work must include:

  1. A complete description of the tool. (E.g. “ChatGPT Version 3.5 via CoCalc’s interface” or Chat-GPT 4 through Bing AI using the Edge browser”, etc.)

  2. A complete record of the queries issued and response provided. (This should be provided as an attachment, appendices, or supplement.)

  3. An attribution statement consistent with the following: “The author generated this <text/code/etc.> in part with <GPT-3, OpenAI’s large-scale language-generation model/etc.> as documented in appendix <1>. Upon generating the draft response, the author reviewed, edited, and revised the response to their own liking and takes ultimate responsibility for the content.”

Academic Integrity#

You are responsible for reading WSU’s Academic Integrity Policy, which is based on Washington State law. If you cheat in your work in this class you will:

  • Fail the course.

  • Be reported to the Center for Community Standards.

  • Have the right to appeal the instructor’s decision.

  • Not be able to drop the course or withdraw from the course until the appeals process is finished.

If you have any questions about what you can and cannot do in this course, ask your instructor.

If you want to ask for a change in the instructor’s decision about academic integrity, use the form at the Center for Community Standards website. You must submit this request within 21 calendar days of the decision.

University Syllabus#

Students are responsible for reading and understanding all university-wide policies and resources pertaining to all courses (for instance: accommodations, care resources, policies on discrimination or harassment), which can be found in the university syllabus.

Students with Disabilities#

Reasonable accommodations are available for students with a documented disability. If you have a disability and need accommodations to fully participate in this class, please either visit or call the Access Center at (Washington Building 217, Phone: 509-335-3417, E-mail: mailto:Access.Center@wsu.edu, URL: https://accesscenter.wsu.edu) to schedule an appointment with an Access Advisor. All accommodations MUST be approved through the Access Center. For more information contact a Disability Specialist on your home campus.

Campus Safety#

Classroom and campus safety are of paramount importance at Washington State University, and are the shared responsibility of the entire campus population. WSU urges students to follow the “Alert, Assess, Act,” protocol for all types of emergencies and the “Run, Hide, Fight” response for an active shooter incident. Remain ALERT (through direct observation or emergency notification), ASSESS your specific situation, and ACT in the most appropriate way to assure your own safety (and the safety of others if you are able).

Please sign up for emergency alerts on your account at MyWSU. For more information on this subject, campus safety, and related topics, please view the FBI’s Run, Hide, Fight video and visit the WSU safety portal.

Students in Crisis - Pullman Resources#

If you or someone you know is in immediate danger, DIAL 911 FIRST!

  • Student Care Network: https://studentcare.wsu.edu/

  • Cougar Transit: 978 267-7233

  • WSU Counseling and Psychological Services (CAPS): 509 335-2159

  • Suicide Prevention Hotline: 800 273-8255

  • Crisis Text Line: Text HOME to 741741

  • WSU Police: 509 335-8548

  • Pullman Police (Non-Emergency): 509 332-2521

  • WSU Office of Civil Rights Compliance & Investigation: 509 335-8288

  • Alternatives to Violence on the Palouse: 877 334-2887

  • Pullman 24-Hour Crisis Line: 509 334-1133