Faculteit  Science and Engineering 
Jaar  2020/21 
Vakcode  WBPH01705 
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 Greensfunction 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 EulerLagrange and Hamilton formalisms to obtain and solve the equations of motion for mechanical systems. 5.setup and solve the equations of motion in noninertial 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 fourvector 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; nonlinear 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, noninertial 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 prerequisite) 

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 


Entreevoorwaarden  The course unit assumes prior knowledge acquired from MechanicsI, Complex analysis, Computational physics in the Bachelor programme (check if the names are still uptodate). 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: Noninertial 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 NAAM12 

Opgenomen in 
