## Admission Requirements

Classical Mechanics a, Introduction to Modern Physics, Electrical and Magnetic Fields, Analysis 1,2 (na) and Linear Algebra 1 (na). The students need to follow the lectures Analysis 3(na) in parallel, unless the material is already known.

## Description

The description of the laws of classical mechanics of Newton are given a more general and more fundamental form in the Lagrange and Hamilton formalisms. This description makes the theory more elegant and more broadly useful. In this form the theory prepares the scene for the treatment of Quantum mechanics.

Subjects to be discussed are: Generalized coordinates; phase space; constraints; Lagrangian and Lagrange’s equations; conservation laws; Hamiltonian and Hamilton’s equations; Hamilton’s principle (principle of least action).

The power of the formalism is illustrated by a second main topic: the analysis of systems of coupled harmonic oscillators. This is a subject of great importance, and examples of problems range from physics, to chemistry, engineering, etc.

## Course objectives

After completing this course the student has gained insight into the importance of the Lagragnge and Hamilton formalism, and into the role of coupled harmonic oscillators in physics. The student is capable of solving problems using the Lagrange and Hamilton formalisms, and problems involving systems of coupled harmonic oscillators. You can apply the concepts to unknown problems.

## Timetable

Schedule

For detailed information go to Timetable in Brightspace

You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudyMap will automatically be displayed in MyTimeTable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.

MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).

For more information, watch the video or go the the 'help-page' in MyTimetable. Please note: Joint Degree students Leiden/Delft have to merge their two different timetables into one. This video explains how to do this.

## Mode of instruction

See Brightspace

Detailed lecture notes are provided, and you are expected to prepare for each lecture by reading the materal (about 8 pages per week).

Exercise classes are orginised in groups. Teaching assistents will offer step-by-step instruction for solving problems, alternated with blocks of time for the students to solve problems, where assistance is constantly offered.

For students interested in more challinging problems and deeper questions we offer an Advanced Physics Track.

The class will be taught in English.

## Assessment method

Written exam with open questions. Part of the exam tests the students' understanding of the theory, the other part tests the skills for independently solving problems. The exam can be retaken.

The grade will be determined from a combination of the exam and the homework exercises.

## Reading list

The prime source of study material are the lecture notes, made available as a pdf document.

For further reading the following books are recommended:

Intermediate dynamics, P. Hamill; Cambridge University Press, 2nd edition, ISBN 978-1009098472

Analytical Mechanics, G.R. Fowles and G.L. Cassiday, 7th edition (Thomson Learning, inc., 2004), ISBN 9780534408138.

Classical Mechanics, H. Goldstein, C.P. Poole Jr., J.L. Safko, 3rd edition (Pearson Education Ltf., 2014), ISBN 9781292026558

## Registration

From the academic year 2022-2023 on every student has to register for courses with the new enrollment tool MyStudyMap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December. Please see this page for more information.

Please note that it is compulsory to both preregister and confirm your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Confirming your exam participation is possible until ten days before the exam.

Extensive FAQ's on MyStudymap can be found here.

## Contact

Contact details of the lecturer: Prof. Dr. D.J. Kraft

## Remarks

none