Advanced Mechanics

Faculteit Science and Engineering
Jaar 2020/21
Vakcode WBPH017-05
Vaknaam Advanced Mechanics
Niveau(s) bachelor
Voertaal Engels
Periode semester I b
ECTS 5
Rooster rooster.rug.nl

Uitgebreide vaknaam Advanced Mechanics
Leerdoelen At the end of the course, the student is able to:
1.solve a general problem with a damped and driven oscillator using the Greens-function technique as well as by using a Fourier expansion.
2.make a numerical simulation of non trivial physical systems and to give a physics interpretation of the results.
3.solve variational problems using the Euler equation with constraints (Lagrange multipliers).
4.apply the Euler-Lagrange and Hamilton formalisms to obtain and solve the equations of motion for mechanical systems.
5.setup and solve the equations of motion in non-inertial systems.
6.solve central force problems and work with the concept of effective potential. He/she can apply the Kepler equations for the orbits.
7.calculate the inertial tensor for a rigid body and use this to calculate the angular momentum and torque for this system.
8.evaluate the stability of solutions by making a small amplitude expansion for perturbations.
9.Be able to write a Lagrangian for a relativistic system in four-vector notation and to be able to derive the equations of motion.
Omschrijving In this course a more abstract formulation of mechanics is developed. In addition the use of numerical methods for solving physics problems is emphasized.
The subjects addressed include:
- Damped and driven oscillators; non-linear effects such as higher harmonics, hysteresis and chaos; Fourier transforms and Green’s functions ;
- Variational calculus; Lagrange multipliers; Hamilton and Lagrange formalism, conservation laws and symmetries, Lagrange density for continuous systems
- Central potentials, Kepler problem,
- Rotating rigid body, non-inertial systems, inertial tensors, Euler angles,
- Relativistic systems, Invariants and fourvector notation, Lagrangian for a particle in an electromagnetic field.
Uren per week
Onderwijsvorm Hoorcollege (LC), Practisch werk (PRC), Werkcollege (T)
(Lectures: 32 hours, Tutorials: 26 hours, Computer practicals: 6 hours, Self study: 76 hours. o participate in the written exam a sufficient mark on all homework problems is a pre-requisite)
Toetsvorm Opdracht (AST), Schriftelijk tentamen (WE)
(Final grade: Written exam with open questions (65%), Two quizzes during lecture hours (10%), Homework assignments (25%).)
Vaksoort bachelor
Coördinator prof. dr. E.A. Bergshoeff
Docent(en) prof. dr. E.A. Bergshoeff
Verplichte literatuur
Titel Auteur ISBN Prijs
Classical Dynamics of Particles and Systems (5th edition).
Thornton & Marion 9780534408961
Entreevoorwaarden The course unit assumes prior knowledge acquired from Mechanics-I, Complex analysis, Computational physics in the Bachelor programme (check if the names are still up-to-date).

The course unit is compulsory for BSc Sterrenkunde (Minor Astronomy) and an elective in the BSc Natuurkunde en Wiskunde (dubbele bachelor), BSc Natuurkunde, richting Nano-, Experimentele en Theoretische Fysica (verdiepende minor Natuurkunde "Science for Scientists"), and BSc Natuurkunde, richting Nano-, Experimentele and Theoretische Fysica (Interessegebied Theoretische Natuurkunde).
Opmerkingen Lecture material (From the book of Marion):
Chapter 6: Variational calculations;
Euler equation, the Brachistochrone problem.
Chapter 7: Hamiltons principle;
Generalized coordinates, Lagrange & Hamilton eq. of motion, conservation theorems
Chapter 8: Central force problem;
Constants of motion, Effective potential, Kepler orbits.
Chapter 9: Dynamics of particles;
Collisions of 2 particles, Cross section.
Chapter 10: Non-inertial reference frame; Coriolis force.
Chapter 12: Coupled oscillators; eigenvectors (als dit niet eerder behandeld is).
Chapter 13: Continuous systems; Loaded string.

This course was registered last year with course code NAAM-12
Opgenomen in
Opleiding Jaar Periode Type
BSc Astronomy  (Minor Astronomy) 3 semester I b keuzegroep
BSc Courses for Exchange Students: Astronomy - Physics - Energy & Environment - semester I b
BSc Mathematics and Physics (double degree) 3 semester I b verplicht
BSc Physics  (Track: Particle Physics) 3 semester I b keuzegroep