Theoretical Physics 1: Classical Mechanics

543 Pages·2016·4.532 MB·English

by  Wolfgang Nolting

Wolfgang Nolting
Theoretical
Physics 1
Classical Mechanics
Theoretical Physics 1

Wolfgang Nolting
Theoretical Physics 1
Classical Mechanics
123
WolfgangNolting
Inst.Physik
Humboldt-UniversitaRtzuBerlin
Berlin,Germany
ISBN978-3-319-40107-2 ISBN978-3-319-40108-9 (eBook)
DOI10.1007/978-3-319-40108-9
LibraryofCongressControlNumber:2016943655
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General Preface
ThesevenvolumesoftheseriesBasicCourse:TheoreticalPhysicsarethoughttobe
textbookmaterialforthestudyofuniversity-levelphysics.Theyareaimedtoimpart,
in a compact form, the most important skills of theoretical physics which can be
usedasbasisforhandlingmoresophisticatedtopicsandproblemsintheadvanced
study of physics as well as in the subsequent physics research. The conceptual
designofthepresentationisorganizedinsuchawaythat
ClassicalMechanics(volume1)
AnalyticalMechanics(volume2)
Electrodynamics(volume3)
SpecialTheoryofRelativity(volume4)
Thermodynamics(volume5)
are considered as the theory part of an integrated course of experimental and
theoretical physics as is being offered at many universities starting from the first
semester.Therefore,thepresentationisconsciouslychosentobeveryelaborateand
self-contained,sometimessurelyatthe costofcertainelegance,sothatthecourse
is suitableevenforself-study,at firstwithoutanyneedof secondaryliterature.At
anystage,nomaterialisusedwhichhasnotbeendealtwithearlierinthetext.This
holds in particular for the mathematical tools, which have been comprehensively
developed starting from the school level, of course more or less in the form of
recipes,suchthatrightfromthebeginningofthestudy,onecansolveproblemsin
theoreticalphysics. The mathematicalinsertionsare always then pluggedin when
theybecomeindispensabletoproceedfurtherintheprogramoftheoreticalphysics.
Itgoeswithoutsayingthatinsuchacontext,notallthemathematicalstatementscan
be proved and derived with absolute rigour. Instead, sometimes a reference must
be made to an appropriate course in mathematics or to an advanced textbook in
mathematics. Nevertheless, I have tried for a reasonably balanced representation
so that the mathematical tools are not only applicable but also appear at least
‘plausible’.
v
vi GeneralPreface
Themathematicalinterludesareofcoursenecessaryonlyinthefirstvolumesof
thisseries,whichincorporatemoreorlessthematerialofabachelorprogram.Inthe
secondpartoftheserieswhichcomprisesthemodernaspectsoftheoreticalphysics,
QuantumMechanics:Basics(volume6)
QuantumMechanics:MethodsandApplications(volume7)
StatisticalPhysics(volume8)
Many-BodyTheory(volume9),
mathematical insertions are no longer necessary. This is partly because, by the
time one comes to this stage, the obligatory mathematics courses one has to take
in order to study physics would have provided the required tools. The fact that
training in theory has already started in the first semester itself permits inclusion
of parts of quantum mechanics and statistical physics in the bachelor program
itself. It is clear that the content of the last three volumes cannot be part of an
integratedcoursebutratherthesubjectmatterofpuretheorylectures.Thisholdsin
particularforMany-BodyTheorywhichisoffered,sometimesunderdifferentnames
as,e.g.,AdvancedQuantumMechanics,intheeighthorsosemesterofstudy.Inthis
part,newmethodsandconceptsbeyondbasicstudiesareintroducedanddiscussed
whicharedevelopedinparticularforcorrelatedmanyparticlesystemswhichinthe
meantime have become indispensable for a student pursuing master’s or a higher
degreeandforbeingabletoreadcurrentresearchliterature.
In all the volumes of the series Basic Course: Theoretical Physics, numerous
exercisesareincludedtodeepentheunderstandingandtohelpcorrectlyapplythe
abstractlyacquiredknowledge.Itisobligatoryforastudenttoattemptonhisown
to adapt and apply the abstract concepts of theoretical physics to solve realistic
problems.Detailed solutionsto the exercisesare givenat the endof eachvolume.
The idea is to help a student to overcomeany difficulty at a particular step of the
solutionortocheckone’sowneffort.Importantlythesesolutionsshouldnotseduce
thestudenttofollowtheeasywayoutasasubstituteforhisowneffort.Attheend
of each biggerchapter,I have addedself-examinationquestionswhich shall serve
asaself-testandmaybeusefulwhilepreparingforexaminations.
I should not forget to thank all the people who have contributed one way or
an other to the success of the book series. The single volumes arose mainly from
lectures which I gave at the universities of Muenster, Wuerzburg, Osnabrueck,
and Berlin in Germany, Valladolid in Spain and Warangal in India. The interest
and constructivecriticism of the students providedme the decisive motivationfor
preparing the rather extensive manuscripts. After the publication of the German
version,Ireceivedalotofsuggestionsfromnumerouscolleaguesforimprovement,
and this helped to further develop and enhance the concept and the performance
of the series. In particular I appreciate very much the support by Prof. Dr. A.
Ramakanth,a long-standingscientific partnerand friend,who helpedme in many
respects,e.g.whatconcernsthecheckingofthetranslationoftheGermantextinto
thepresentEnglishversion.
GeneralPreface vii
SpecialthanksareduetotheSpringercompany,inparticulartoDr.Th.Schneider
and his team. I remember many useful motivations and stimulations. I have the
feelingthatmybooksarewelltakencareof.
Berlin,Germany WolfgangNolting
May2015

Preface to Volume 1
The first volume of the series Basic Course: Theoretical Physics presented here
dealswithClassicalMechanics,atopicwhichmaybedescribedas
analysisofthelawsandrulesaccordingtowhichphysicalbodiesmoveinspaceandtime
undertheinfluenceofforces.
This formulation already contains certain fundamental concepts whose rigorous
definitions appear rather non-trivial and therefore have to be worked out with
sufficientcare.Inthecaseofafewofthesefundamentalconcepts,wehavetoeven
accept them, to start with, as more or less plausible facts of everyday experience
withoutgoingintotheexactphysicaldefinitions.Weassumeamaterialbodytobe
anobjectwhichislocalizedinspaceandtimeandpossessesan(inertial)mass.The
conceptisstilltobediscussed.Thisisalsovalidfortheconceptofforce.Theforces
are causing changes of the shape and/or in the state of motion of the body under
consideration. What we mean by space is the three-dimensional Euclidean space
beingunrestrictedinallthethreedirections,beinghomogeneousandisotropic,i.e.
translationsorrotationsofourworldasawholeinthisspacehavenoconsequences.
The time is also a fact of experience from which we only know that it does exist
flowing uniformly and unidirectionally. It is also homogeneous which means no
pointintimeisapriorisuperiorinanymannertoanyotherpointintime.
In order to describe natural phenomena, a physicist needs mathematics as
language. But the dilemma lies in the fact that theoretical mechanics can be
impartedinaproperwayonlywhenthenecessarymathematicaltoolsareavailable.
If theoretical physics is started right in the first semester, the student is not yet
equipped with these tools. That is why the first volume of the Basic Course:
Theoretical Physics begins with a concise mathematical introduction which is
presented in a concentrated and focused form including all the material which is
absolutelynecessaryforthedevelopmentoftheoreticalclassicalmechanics.Itgoes
without saying that in such a context not all mathematicaltheories can be proved
or derived with absolute stringency and exactness. Nevertheless, I have tried for
a reasonably balanced representation so that mathematical theories are not only
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