WiSe2020/21. Theoretical Physics I: Theoretical Mechanics


2021 03 24      The retake exam and another tutorial for questions concerning the retake habe been (re-)scheduled to
          tutorium on Wed, 9 April 2021 at 4pm
          retake exam on Wed, 14 April 2021 at 1pm
2021 01 27      Exercise sheet 10 is available now.
2021 01 20      The wiki discussion pages are also online now. While preparing the wiki pages I clarified a few issues in the questions. Hence, also the PDF file has been updated with respect to the initial version!
2021 01 19      The nineth exercise sheet is available as a PDF file (790 kB).
2021 01 12      The eigth exercise sheet is available as a PDF file (160 kB). The wiki discussion pages are also online now.
Watch out: while preparing the wiki pages I corrected a number of misprints. Hence, also the PDF file has been updated with respect to the initial version!
2020 12 15      The seventh exercise sheet is available as a PDF file (330 kB). The wiki discussion pages will follow shortly.
2020 12 08      The sixth exercise sheet is available as a PDF file (170 kB). The wiki discussion pages will follow shortly.
2020 12 01      The fifth exercise sheet is available as a PDF file (950 kB). The wiki discussion pages will follow shortly.
2020 11 24      The fourth exercise sheet is available as a PDF file (950 kB), and the wiki discussion pages are also open.
2020 11 17      The third exercise sheet is available as a PDF file (330 kB). The wiki discussion pages will follow shortly.
2020 11 11      In an update to second exercise sheet I corrected typos and consistently introduced the nomenclature adopted in the lecture notes. Moreover, the discussion forums for the problems have been implemented in the Wiki.
Please post a question in the wiki whenever it is not clear what should be done!
2020 11 10      I uploaded the second exercise sheet. It should be solved by the end of the weekend.
2020 11 05      The wiki is now accessible via the page https://www.physik.uni-leipzig.de/jvwikis/mechanics/. To use the new login page you might have to refresh the page in your browser, or (in the worst case) remove the cookie for the page access.
2020 10 31      You can enter the wiki via the wiki login page.
2020 10 31      I uploaded the first exercise sheet. It should be solved by the end of the week.
2020 10 31      Due to a security feature of our web server I can not yet make the wiki accessible to you. I am working on it...
2020 10 31      Starting from next Tuesday we will have online lectures on Tuesday and Thursday via this BigBlueButton Channel. The access code will be provided on the Wiki.
2020 10 20      I updated the lecture notes. There are changes in the layout, and I corrected typos.
2020 10 14      Registeration for the seminars will be possible till be beginning of November. Presently, we are still working out issues with rooms and broadcasting.

Topic Overview

We will come to know different approaches to determine the classical equations of motion of mechanical systems, and to discuss the features of the solutions of these equations. The following topics will be covered

Mathematical Methods.     Vectors, coordinates, complex numbers, equations of motion, conservation laws
basics of variational calculus, solutions of differential equations
Newtonian mechanics. axioms, Galileo-transformations, phase space
Lagrange mechanics. derivation, equations of motion
Model systems. motion of planets and asteroids: Kepler problem
solid bodies: center of mass, rotation, reflection

Supplementary literature, animations, programs


David Morin     Introduction to Classical Mechanics (Cambridge, 2007)
an elaborate introduction with a lot of worked exercises
our lectures will cover (al most) the chapters 1–8
John R. Taylor     Classical Mechanics (Univ. Science Books, 2005)
our lectures will cover (al most) the chapters 1–9
Siegfried Großmann     Mathematischer Einführungskurs für die Physik (Springer, 2012)
lucit introduction to mathematical concepts in physics — unfortunately on available in German
Leonard Susskind, George Hrabovsky     The Theoretical Minimum: Classical Mechanics (Penguin, 2013)
a hero of quantum field theory and a science journalist develop a course for interested laymen
with Youtube-Channel and extensive support page

Internet Ressources

Real World Physics Problems with lots of idea, animations, and excellent explanations
Mathematical Impressions of the Simons Foundation features excellent movies on Applied Mathematics and Physics
Thomas Hempels Web-Seiten     Notes and Exercises on "Mathematischen Methoden der Naturwissenschaften" (in German, sorry!)
a large number of lecture notes, and a huge amount of exercises on the level of the course and beyond
Franz-Josef Elmers Pendulum Lab     Interaktive simulations of the motions of pendula with a splendit Lecture Room
PhET Interactive Simulations     interaktive simulations on many topics in mathematics and science
animations and interactive training on many topcs of the course, check out for instance Masses and Springs

Sage, Python, and PhyPhox

Python and Sage will be used for numerical studies and visualization. The script files are notebooks that run interactively in Jupyter. Please store them on your computer, start Jupyter, and then open the notebook. The files contain absolutely minimalistic explanations and comments. I assume that you know what they are intended to do because we discussed the problems in a seminar or in class.

As introductions to Python and Sage I recommend the books Steward: "Python for Scientists" and Zimmermann u.a.: "Computational Mathematics with SageMath".

At times I will also use PhyPhox to illustrate the relation between observations, models and theory.

Lecture Notes

I am striving to TeΧ my lecture notes. The present state of this project is available here. Help is greatly appreciated. I offer guest access to the full project such that you get access to the files, follow tickets, open issues, and submit contributions to the project. Please register at the GitLab Server of the University, and contact me if you wish to participate.

Home Work Problems

In subsequent weeks it will be ready by Wednesday such that there is the opportunity for feedback on Thursday.

Date    Topic    PDF       
2020 10 31      1. Dimensions/Groups      (PDF, 200kB) »
2020 11 10      2. Vectors/Forces      (PDF, 250kB) »
2020 11 17      3. Vectors/Particle Tracks      (PDF, 330kB) »
2020 11 24      4. Derivatives/Gradients/Constants of Motion      (PDF, 270kB) »
2020 12 01      5. Newton's Laws, Conservation Laws      (PDF, 950kB) »
2020 12 08      6. Solving ODEs: integration and separation of variables      (PDF, 170kB) »
2020 12 15      7. ODEs, phase space plots, Taylor expansion      (PDF, 330kB) »
2021 01 12      8. Eigenvalues and eigenvectors      (PDF, 160kB) »
2021 01 19      9. Lagrange formalism      (PDF, 790kB) »
2021 01 27      10. Lagrange formalism 2      (PDF, 1.4MB) »

Lectures, Seminars, and Tutorials

Due to the present circumstances lectures can only be delivered online presently:
    Lectures           Tue 13:15 – 15:00      BigBlueButton Channel
          Thu   13:15 – 15:00      BigBlueButton Channel
For an open discussion concerning questions and problems I offer an additional
    Tutorial           Fri 17:15 – open end      BigBlueButton Channel
There also will be seminars where the homework exercises are discussed. The time slots for these events will be arranged in mutual agreement.

Please work in teams to discuss the material covered in the class and the homework assignments. The aim of these discussions should be to reach an understanding that allows you to formulate your own solution to the problem. The corrections of the submitted exercises are a feedback how well you understand the topic, and how well you perform in formulating your solutions. It is necessary for you to pass the exam. Your perfomance helps me to figure out how well you can follow my lectures, and make me aware of issues that need additional attention in the lectures.

I found some students who are interested to serve as student buddies for the course. They are willing to interact with you about the lectures and provide help with the exercises. More information will be provided on the wiki.


There will be open-book exams on
         Friday, 19 Feb 2021      at 1 pm
Wednesday,     9 April 2021      at 1 pm