We have planned this class partly as a flipped class where we would like to
- use Mondays as regular lecture days
- Wednesdays as a mix of lectures and problem solving (or just one of them depending on needs and feedback from you). The first two weeks we will lecture both Monday and Wednesday.
- Fridays are planned as flipped classes, with problem solving and more.
We will have at our disposal room 2202 in the new STEM building.
The lectures are in person but will be available online as well via zoom. This will be done throughout the semester. It means that if you cannot be there physically (for many reasons), you can always attend via zoom. All lectures will be recorded and uploaded and made available to you via D2L and the website of the course.
We will thus have in-person classes and the lectures/sessions will be
- made available to everybody via zoom as we teach (hybrid mode), you can attend from wherever you want. Zoom has also live transcripts of the direct lecture;
- the videos will be posted right afterwards in case you could not attend (that is the video of the actual lecture, it is like a kind of podcast with movie). You can thus review the material which was discussed in peace whenever you want;
- We use always a whiteboard (iPad) instead of a blackboard and these handwritten notes are also posted after the lectures;
- We have extensive online material, lecture notes, exercises, projects and more, see the GitHub site of the course at https://github.com/mhjensen/Physics321, see https://mhjensen.github.io/Physics321/doc/LectureNotes/_build/html/chapter1.html for the online textbook and https://mhjensen.github.io/Physics321/doc/web/course.html for the weekly material.
- We are going to make shorter videos which cover various topics and how to solve different exercises and more. They will be posted as we move on during the semester;
We have also created a Slack channel, see the link here to join https://join.slack.com/t/classicalmech-qzd7435/shared_invite/zt-1n2ynisck-C_dQ7X67VpRDPqZGOvYzhA You can also use https://classicalmech-qzd7435.slack.com
Here you will find a general overview of the course, with learning outcomes, teaching schedule etc.
Lectures | Location | ||
---|---|---|---|
Monday 3:00-3:50pm | Wednesday 3:00-3:50pm | Friday 3:00-3:50pm | Room 2202 STEM building and digital (see zoom link below) |
Instructor | Office | Office phone/cellphone | |
---|---|---|---|
Morten Hjorth-Jensen https://github.com/mhjensen | hjensen@msu.edu | Office: NSCL/FRIB 2131 | 5179087290/5172491375/ |
Zoom link for lectures | Meeting ID | Passcode |
---|---|---|
https://msu.zoom.us/j/91523293661?pwd=akpyelF3dDBlQy9vVm4xN3pmd1BQdz09 | 915 2329 3661 | Passcode: 739577 |
Office Hours for Morten | |
---|---|
Monday/Wednesday/Friday 4-5:00pm | or immediately after class |
Teaching assistant | Office Hour | Zoom Link | |
---|---|---|---|
Shuyue Xue | xueshuy1@msu.edu | Thursday 1.00-2.00pm | https://msu.zoom.us/j/8131454131 (Passcode: 8131) |
Learning Assistant | Office Hour | Where | |
---|---|---|---|
Abby Baratta | baratta2@msu.edu | Thursdays 10am-12pm | Helproom BPS |
Additional office hour by Morten | Zoom link |
---|---|
Tuesdays 8pm-9pm | Same as lecture link above |
Activity | Percentage of total score |
---|---|
Homeworks, 9 in total and due Fridays the week after | 20% |
First Midterm Project, due Friday March 3 | 25% |
Second Midterm Project, due Friday April 14 | 25% |
Final Exam project, due Friday May 5 | 30% |
Extra Credit Assignment, homework 10, (due Monday May 1) | 10% |
Grading scale | ||||||
---|---|---|---|---|---|---|
4.0(90%) | 3.5(80%) | 3.0(70%) | 2.5(60%) | 2.0(50%) | 1.5(40%) | 1.0(30%) |
Recommended textbook:
- JRT: John R. Taylor, Classical Mechanics (Univ. Sci. Books 2005), https://uscibooks.aip.org/books/classical-mechanics/, see also https://github.com/mhjensen/Physics321/tree/master/doc/Literature Additional textbooks:
- AMS: Anders Malthe-Sørenssen, Elementary Mechanics using Python (Springer 2015), https://www.springer.com/gp/book/9783319195957 and https://github.com/mhjensen/Physics321/tree/master/doc/Literature
- Lecture notes: Posted lecture notes are in the doc/pub folder here or at https://mhjensen.github.io/Physics321/doc/web/course.html for easier viewing. They are not meant to be a replacement for textbook. These notes are updated on a weekly basis and a git pull should thus always give you the latest update.
Weekly mails (Weekends/Mondays) with updates, plans for lectures etc will be sent to everybody before the week begins.
- Monday 1/9: Introduction to the course and reminder on vectors, space, time and motion, JRT chapters 1.2 and 1.3 and lecture notes (https://mhjensen.github.io/Physics321/doc/pub/week2/html/week2.html). Python programming reminder, elements from CMSE 201 and how they are used in this course. Installing software (anaconda). See slides at https://mhjensen.github.io/Physics321/doc/pub/week2/html/week2.html).
AMS chapters 2 and 4 are very useful. 1st homework due January 21.
- Lecture video at https://youtu.be/BT2pSnYNYHE
- Handwritten notes from lecture at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesJanuary9.pdf
- Wednesday 1/11: Forces and Newton's laws of motion. Free fall problems. JRT chapter 1.4 and lecture notes (https://mhjensen.github.io/Physics321/doc/pub/week2/html/week2.html). AMS chapters 2 and 4 are very useful.
- Lecture video at https://youtu.be/s-cqtSfOZ1Q
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesJanuary11.pdf
- Friday 1/13: Discussions and problem solving and discussion of first homework.
- Short video on practicalities about exercises and the Friday sessions https://youtu.be/Rt5q3uFQGsk
-
Monday 1/16: MLK day, no classes
-
Wednesday 1/18: Motion and forces, Newton's laws, examples.
- Handwritten notes from lecture at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesJanuary18.pdf
- Video of lecture at https://youtu.be/-nfzGH56v_w
-
Friday 1/20: Motion and forces, Newton's laws, examples. Problems solving. Deadline first homework.
- Video of first 20 min at https://youtu.be/iLX21OKuhp0
-
Good reads are Taylor chapters 1.4, 1.5, 1.6, 2.1-2.4 and AMS chapters 4.2 and 5 and and lecture notes (https://mhjensen.github.io/Physics321/doc/pub/week3/html/week3.html).
-
Solution to first hw at https://github.com/mhjensen/Physics321/tree/master/doc/Homeworks/Solutions
- Monday 1/24: We discuss various forces and their pertinent equations of motion. Recommended reading: Taylor 2.1-2.4. Malthe-Sørenssen chapter 6-7 contains many examples. We will cover in particular a falling object in two dimensions with linear air resistance relevant for homework 3.
- Video of lecture at https://youtu.be/Izx1W4qqgmo
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesJanuary23.pdf
- Wednesday 1/25: We discuss other force models with examples such as the gravitational force and a spring force. See Malthe-Sørenssen chapter 7.3-7.5. We start also our discussion of energy and work, see Taylor 4.1
- Video of lecture at https://youtu.be/f9hqy6o6XCg
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesJanuary25.pdf
- Friday 1/27: We discuss several examples of energy and work. Taylor 4.1-4.3. Problem solving. Deadline second homework.
- Video of exercise session at https://youtu.be/MDO5fe2Rw70
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesJanuary27.pdf
- Solution to second hw at https://github.com/mhjensen/Physics321/tree/master/doc/Homeworks/Solutions
- Monday 1/30: Work energy theorem, conservative forces and momentum conservation, 4th homework available
- Video with subtitles at https://youtu.be/H_TuYjM9csk
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesJanuary30.pdf
- Wednesday 2/1: Examples of applications of conservation laws, angular momentum conservation.
- Video of lecture at https://youtu.be/t_bStzWIVJY
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesFebruary1.pdf
- Friday 2/3: Conservation laws and problem solving. Deadline third homework.
- Video of exercise session, first 20 min, hints for exercises 5 and 6 at https://youtu.be/SN6Rms9LlNs
- Good reads are Taylor sections 3.1-3.5 and 4.1-4.3 and AMS chapters 10-14.
- Solution to third hw at https://github.com/mhjensen/Physics321/tree/master/doc/Homeworks/Solutions
- Monday 2/6: Conservation laws and examples.
- Video of lecture at https://youtu.be/plcIWuGXoms
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesFebruary6.pdf
- Wednesday 2/8: Examples of application of conservations laws (see chapter 4 of Taylor).
- Video of lecture at https://youtu.be/iKtX3EIzb0A
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesFebruary8.pdf
- Friday 2/10: Discussion of fourth homework. Deadline fourth homework.
- Taylor chapter 4 is the essential reading. See also chapter 7 of Malthe-Sørenssen for exercise 6 in homework 4
- Video with hints and tips for hw 4 at https://youtu.be/nTQSb7-5xy0
- Solution to fourth hw at https://github.com/mhjensen/Physics321/tree/master/doc/Homeworks/Solutions
- Monday 2/13: Discussion of conditions for conservative forces and summing up our
discussion on conservative forces. Discussion of potential surfaces and their interpretations. Start discussion of harmonic oscillations.
- Reading suggestion: Taylor sections 4.6, 4.9, 4.10 and 5.1 and 5.2 on harmonic oscillations and lecture notes
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesFebruary13.pdf
- Video of lecture at https://youtu.be/3GCGhSN4nIw
- Wednesday 2/15: The Earth-Sun problem and energy-conserving algorithms and how to encode in more efficient ways various algorithms for solving the equations of motion (Euler, Euler-Cromer and Velocity Verlet).
- Reading suggestions: Taylor section 4.8 and lecture notes
- Friday 2/17: Working on the Earth-Sun problem and hw 5.
- Reading suggestions: Taylor chapters 3 and 4 and lecture notes
- Solution to fifth hw at https://github.com/mhjensen/Physics321/tree/master/doc/Homeworks/Solutions
- Monday 2/20: Harmonic oscillations and Damped Oscillations. Reading suggestions Taylor 5.1-5.3
- Video of Lecture at https://youtu.be/3otwJIm796s
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesFebruary20.pdf
- Wednesday 2/22: Damped oscillations
- Video of Lecture at https://youtu.be/Y1QfsBplX9k
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesFebruary22.pdf
- Friday 2/24: Discussion of first midterm.
- Good reads are sections 5.4-5.7 of Taylor on oscillations.
- First midterm project, available Feb 20 and due March 3, 2023
- Video with hints and tips for first midterm https://youtu.be/9rLx7MdLWs0
- Monday 2/27: Damped and driven oscillations
- Video of lecture at https://youtu.be/39bqKrnEddk
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesFebruary27.pdf
- Wednesday 3/1: Discussions of oscillations and time-dependent forces. Discussion of first midterm.
- Video of lecture at https://youtu.be/OeaBq13izhM
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesMarch1.pdf
- Friday 3/3: Discussion of first midterm. Deadline for first midterm.
- Solution to first midterm hw at https://github.com/mhjensen/Physics321/tree/master/doc/Homeworks/Solutions. See also codes for part 1 and part 2 in the same folder.
- Monday 3/13: Harmonic oscillations, damping and driven oscillations
- Video of lecture at https://youtu.be/3j2xxCGcqs4
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesMarch13.pdf
- Wednesday 3/15: Harmonic oscillations, damping and driven oscillations
- Video of lecture at https://youtu.be/McYxOqDvOO4
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesMarch15.pdf
- Video on solving differential equations numerically at https://youtu.be/7nYIfV0z1VM
- Video on Fourier aanalysis at https://youtu.be/neXZ4fb-4Rs
- Friday 3/17: Discussion and work on homework 6. Deadline sixth homework.
- Reading suggestions for week 11: Taylor sections 5.6-5.8 and lecture notes at URL:"https://mhjensen.github.io/Physics321/doc/pub/week10/html/week10-reveal.html"
- Short video at https://youtu.be/WqqD4zel-zg
- Solution to sixth hw at https://github.com/mhjensen/Physics321/tree/master/doc/Homeworks/Solutions
- Monday 3/20: Two-body problems and gravitational forces. Definition of the two-body problem, rewriting the equations in relative and center-of-mass coordinates
- Reading suggestion: Taylor sections 8.2-8.3 and lecture notes
- Video of lecture at https://youtu.be/z2jyJI-dryg
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesMarch20.pdf
- Wednesday 3/21: Preparing the ground for the gravitional force and its solution in two dimensions
- Video of lecture at https://youtu.be/Di-WVWTjKuw
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesMarch22.pdf
- Reading suggestion: Taylor chapter 8.4 and lecture notes
- Friday 3/24: Summary and discussions of two-body problems and work on homework 7. Deadline seventh homework.
- Solution to seventh homework at https://github.com/mhjensen/Physics321/tree/master/doc/Homeworks/Solutions
- Monday 3/27: Computational topics: functions and classes, the harmonic oscillator as warm-up case
- Reading suggestion: Lecture notes and Taylor section 8.4
- Video of lecture at https://youtu.be/SIaY-RTV4VE
- Handwritten notes for lecture at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesMarch27.pdf
- Wednesday 3/29: Discussion of elliptical orbits and Kepler's laws
- Reading suggestion: lecture notes and Taylor sections 8.5-8.6
- Video of lecture at https://youtu.be/TlcHXrzVY-I
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesMarch29.pdf
- Friday 3/31: Summary of week and discussion of homework 8
- Video of lecture at https://youtu.be/uTvuXu5J1N0
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesMarch31.pdf
- Solution to eighth hw at https://github.com/mhjensen/Physics321/tree/master/doc/Homeworks/Solutions
-
Monday 4/3: Physical interpretation of various orbit types
- Reading suggestions: lecture notes and Taylor section 8.5-8.8. Second midterm available April 3
- Video of lecture at https://youtu.be/HwaxZFeJ4eg
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesApril3.pdf
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Wednesday 4/5: Discussion of second midterm, hints and tips plus Kepler orbit analysis
- Video of Lecture at https://youtu.be/xnMIkLE_rzM
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesApril5.pdf
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Friday 4/7: Summary of week and discussion of and work on second midterm. Deadline 2nd midterm is April 15
- Video at https://youtu.be/_JZbimHBwSI with hints for part 2.
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesApril7.pdf
- Monday 4/10: Lagrangian formalism
- Reading suggestion: Lecture notes and Taylor sections 6.1-6.4
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesApril10.pdf - Video of lecture at https://youtu.be/Sfkdnq9JKB8
- Wednesday 4/12: Lagrangian formalism, derivation of the Euler-Lagrange equations
- Reading suggestions: lecture notes and Taylor sections 6.1-6.4
- Video of lecture at https://youtu.be/vNKn1HyC9kw
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesApril12.pdf
- Friday 4/14: Summary of week and work on second midterm. Deadline second midterm.
- Solution to second midterm hw at https://github.com/mhjensen/Physics321/tree/master/doc/Homeworks/Solutions.
- Monday 4/17: Lagrangian formalism and Variational Calculus
- Reading suggestions: lecture notes and Taylor sections 6.1-6.4
- Video of lecture at https://youtu.be/IwVDDlQgJ60
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesApril17.pdf
- Wednesday 4/19: Euler-Lagrange equations and the Lagrangian with examples and Principle of Least Action
- Video of lecture at https://youtu.be/f_Kwaf_W8WU
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesApril19.pdf
- Reading suggestions: lecture notes and Taylor sections 6.3-6.4
- Friday 4/21: Work on homework nine. Deadline ninth homework April 28.
- Solution to ninth hw at https://github.com/mhjensen/Physics321/tree/master/doc/Homeworks/Solutions
- Monday 4/24: Lagrangian formalism and discussion of final from 2022
- Video of lecture at https://youtu.be/YwVy79eJ8uU
- Handwritten notes at https://github.com/mhjensen/Physics321/blob/master/doc/HandWrittenNotes/Spring2023/NotesApril24.pdf
- Wednesday 4/26: Summary of course and discussion of final
- Video of lecture at https://youtu.be/k-C6FU3hzNQ
- Friday 4/28: Discussion and work on final project
Depending on your availability, we can have at least two sessions in order to discuss the final project.
- Final Exam: The final exam will be a project similar to the two midterm projects. Deadline May 5 at midnight.
After the course you should:
- be able to analyze forces that act on objects, apply Newton’s laws to determine the equations of motion, and solve these analytically and numerically,
- Know about inertial frames and their relation to accelerating and rotating frames (non-inertial frames)
- Know about forces, work, energy, angular momentum, linear momentum and conservation laws
- Know about various types of motions, falling objects, objects moving in various fields
- Know how to analyze energy diagrams and defining effective potential
- Have knowledge about small oscillations, Harmonic oscillator potential and equations of motion
- Have knowledge about transformation of variables that allow for analytical solutions, example two-body problems
- Have knowledge about central forces and two-body problems, center-of-mass and relative coordinates as reference frame
- Have knowledge about two-body scattering problems, classical scattering cross section
- Have knowledge about Variational calculus and Lagrangian formalism
- Know how to derive the equations of motion from the Lagrangian formalism with and without constraints (Lagrangian multipliers)
To solve many of these problems, we have through different projects and weekly exercises studied many systems numerically, from falling objects with and without friction/air resistance, small oscillations (harmonic oscillator), gravitational problems and other central force problems, rotations and the classical pendulum. To solve these systems, we have applied different algorithms for solving differential equations. These are
- Euler-Cromer and Velocity-Verlet as energy conserving algorithms (time-independent forces)
- Runge-Kutta family of algorithms for time-dependent forces We have also, in connection with for example the work-energy theorem studied methods for evaluating integrals. These are
- Numerical integration using the Trapezoidal, midpoint and Simpson's rule.
You should also have acquired skills in structuring a numerical project, as well as having developed a critical understanding of the pros and cons of the methods and an understanding of their limits and what can go wrong. Computing means solving scientific problems using computers. It covers numerical as well as symbolic computing. Computing is also about developing an understanding of the scientific process by enhancing algorithmic thinking when solving problems. Computing competence has always been a central part of the science and engineering education. In particular, some of the competences that are important in the development of your own understanding of computations, we would like to emphasize
- derivation, verification, and implementation of algorithms
- understanding what can go wrong with algorithms
- overview of important, known algorithms for solving mechanics problems (To a extent large differential equations and integration)
- understanding how algorithms are used to solve mathematical problems
- Making science (your results) reproducible
- algorithmic thinking for gaining deeper insights about scientific problems