Fundamental Principles of Classical Mechanics PDF ePub eBook

Books Info:

Fundamental Principles of Classical Mechanics free pdf This book is written with the belief that classical mechanics, as a theoretical discipline, possesses an inherent beauty, depth, and richness that far transcends its immediate applications in mechanical systems. These properties are manifested, by and large, through the coherence and elegance of the mathematical structure underlying the discipline, and are eminently worthy of being communicated to physics students at the earliest stage possible. This volume is therefore addressed mainly to advanced undergraduate and beginning graduate physics students who are interested in the application of modern mathematical methods in classical mechanics, in particular, those derived from the fields of topology and differential geometry, and also to the occasional mathematics student who is interested in important physics applications of these areas of mathematics. Its main purpose is to offer an introductory and broad glimpse of the majestic edifice of the mathematical theory of classical dynamics, not only in the time-honored analytical tradition of Newton, Laplace, Lagrange, Hamilton, Jacobi, and Whittaker, but also the more topological/geometrical one established by Poincare, and enriched by Birkhoff, Lyapunov, Smale, Siegel, Kolmogorov, Arnold, and Moser (as well as many others).Contents: Vectors, Tensors, and Linear TransformationsExterior Algebra: Determinants, Oriented Frames and Oriented VolumesThe Hodge-Star Operator and the Vector Cross ProductKinematics and Moving Frames: From the Angular Velocity to Gauge FieldsDifferentiable Manifolds: The Tangent and Cotangent BundlesExterior Calculus: Differential FormsVector Calculus by Differential FormsThe Stokes TheoremCartan's Method of Moving Frames: Curvilinear Coordinates in ?3Mechanical Constraints: The Frobenius TheoremFlows and Lie DerivativesNewton's Laws: Inertial and Non-inertial FramesSimple Applications of Newton's LawsPotential Theory: Newtonian GravitationCentrifugal and Coriolis ForcesHarmonic Oscillators: Fourier Transforms and Green's FunctionsClassical Model of the Atom: Power SpectraDynamical Systems and Their StabilitiesMany-Particle Systems and the Conservation PrinciplesRigid-Body Dynamics: The Euler-Poisson Equations of MotionTopology and Systems with Holonomic Constraints: Homology and de Rham CohomologyConnections on Vector Bundles: Affine Connections on Tangent BundlesThe Parallel Translation of Vectors: The Foucault PendulumGeometric Phases, Gauge Fields, and the Mechanics of Deformable Bodies: The "Falling Cat" ProblemForce and CurvatureThe Gauss-Bonnet-Chern Theorem and HolonomyThe Curvature Tensor in Riemannian GeometryFrame Bundles and Principal Bundles, Connections on Principal BundlesCalculus of Variations, the Euler-Lagrange Equations, the First Variation of Arclength and GeodesicsThe Second Variation of Arclength, Index Forms, and Jacobi FieldsThe Lagrangian Formulation of Classical Mechanics: Hamilton's Principle of Least Action, Lagrange Multipliers in Constrained MotionSmall Oscillations and Normal ModesThe Hamiltonian Formulation of Classical Mechanics: Hamilton's Equations of MotionSymmetry and ConservationSymmetric TopsCanonical Transformations and the Symplectic GroupGenerating Functions and the Hamilton-Jacobi EquationIntegrability, Invariant Tori, Action-Angle VariablesSymplectic Geometry in Hamiltonian Dynamics, Hamiltonian Flows, and Poincare-Cartan Integral InvariantsDarboux's Theorem in Symplectic GeometryThe Kolmogorov-Arnold-Moser (KAM) TheoremThe Homoclinic Tan

About Kai S Lam

Regrettably, at this time we cannot give you information regarding this Founder Kai S Lam. However, this does not necessarily mean we are unsuccessful on her behalf variety. We also request that you simply allow us to on this make a difference. If you have sparetime and desire will certainly profoundly enjoy in case you give all of us your information. When receiving these kinds of comments and info from end users about the Fundamental Principles of Classical Mechanics Publisher Kai S Lam, most of us initially your ex examine. After we make sure that just about all correct, only article it. We fully grasp this enable and also thanks in advance.

Details Book

Author : Kai S Lam
Publisher : World Scientific Publishing Company
Data Published : 02 July 2014
ISBN : 9814551503
EAN : 9789814551502
Format Book : PDF, Epub, DOCx, TXT
Number of Pages : 592 pages
Age + : 15 years
Language : English
Rating :

Reviews Fundamental Principles of Classical Mechanics



17 Comments Add a comment




Related eBooks Download


  • Mathematical Methods of Classical Mechanics free pdfMathematical Methods of Classical Mechanics

    In this text. the author constructs the mathematical apparatus of classical mechanics from the beginning. examining all the basic problems in dynamics. including the theory of oscillations. the theory of rigid body motion..


  • Applications of Contact Geometry and Topology in Physics free pdfApplications of Contact Geometry and Topology in Physics

    Although contact geometry and topology is briefly discussed in V I Arnol'd's book "Mathematical Methods of Classical Mechanics" (Springer-Verlag. 1989. 2nd edition). it still remains a domain of research in pure mathematics..


  • Differential Geometry free pdfDifferential Geometry

    Bundles. connections. metrics and curvature are the 'lingua franca' of modern differential geometry and theoretical physics. This book will supply a graduate student in mathematics or theoretical physics with the fundamentals of these objects..


  • Geometry from Dynamics, Classical and Quantum free pdfGeometry from Dynamics, Classical and Quantum

    This book describes. by using elementary techniques. how some geometrical structures widely used today in many areas of physics. like symplectic. Poisson. Lagrangian..


  • Initial Boundary Value Problems in Mathematical Physics free pdfInitial Boundary Value Problems in Mathematical Physics

    The lectures presented in this book were given at the University of Bonn in the academic year 1983/4 and in part at the University of Strathclyde. Glasgow. Their aim was to introduce graduate students of both mathematics and physics to the time dependent theory of linear equations of mathematical physics and to classical scattering theory..


  • Fundamental Principles of Classical Mechanics free pdfFundamental Principles of Classical Mechanics

    . This book is written with the belief that classical mechanics, as a theoretical discipline, possesses an inherent beauty, depth, and richness that far transcends its immediate applications in mechan