04149nam a22005175i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001700167072002300184082001500207100003000222245008800252264007100340300004500411336002600456337002600482338003600508347002400544490007900568505097000647520145901617650001703076650002703093650002603120650001303146650001503159650001203174650002503186650001703211650002703228650001503255650002603270650002903296650005203325650003703377710003403414773002003448776003603468830007903504856004803583978-0-8176-8352-8DE-He21320180115171445.0cr nn 008mamaa120928s2012 xxu| s |||| 0|eng d a97808176835287 a10.1007/978-0-8176-8352-82doi 4aQA641-670 7aPBMP2bicssc 7aMAT0120302bisacsh04a516.362231 aAntonio, Romano.eauthor.10aClassical Mechanics with Mathematica®h[electronic resource] /cby Romano Antonio. 1aBoston, MA :bBirkhäuser Boston :bImprint: Birkhäuser,c2012. aXIV, 506 p. 127 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aModeling and Simulation in Science, Engineering and Technology,x2164-36790 aI Introduction to Linear Algebra and Differential Geometry.- 1 Vector Space and Linear Maps.- 2 Tensor Algebra.- 3 Skew-symmetric Tensors and Exterior Algebra.- 4 Euclidean and Symplectic Vector Spaces.- 5 Duality and Euclidean Tensors.- 6 Differentiable Manifolds.- 7 One-Parameter Groups of Diffeomorphisms.- 8 Exterior Derivative and Integration.- 9 Absolute Differential Calculus -- 10 An Overview of Dynamical Systems.- II Mechanics.- 11 Kinematics of a Point Particle.- 12 Kinematics of Rigid Bodies.- 13 Principles of Dynamics.- 14 Dynamics of a Material Point.- 15 General Principles of Rigid Body Dynamics.- 16 Dynamics of a Rigid Body.- 17 Lagrangian Dynamics.- 18 Hamiltonian Dynamics.- 19 Hamilton-Jacobi Theory.- 20 Completely Integrable Systems.- 21 Elements of Statistical Mechanics of Equilibrium.- 22 Impulsive Dynamics.- 23 Introduction to Fluid Mechanics -- A First-Order PDE.- B Fourier’s Series.- References.- Index. aThis textbook takes a broad yet thorough approach to mechanics, aimed at bridging the gap between classical analytic and modern differential geometric approaches to the subject. Developed by the author from 35 years of teaching experience, the presentation is designed to give students an overview of the many different models used through the history of the field—from Newton to Lagrange—while also painting a clear picture of the most modern developments. Throughout, it makes heavy use of the powerful tools offered by Mathematica® . The volume is organized into two parts. The first focuses on developing the mathematical framework of linear algebra and differential geometry necessary for the remainder of the book. Topics covered include tensor algebra, Euclidean and symplectic vector spaces, differential manifolds, and absolute differential calculus. The second part of the book applies these topics to kinematics, rigid body dynamics, Lagrangian and Hamiltonian dynamics, Hamilton–Jacobi theory, completely integrable systems, statistical mechanics of equilibrium, and impulsive dynamics, among others. With a unique selection of topics and a large array of exercises to reinforce concepts, Classical Mechanics with Mathematica is an excellent resource for graduate students in physics. It can also serve as a reference for researchers wishing to gain a deeper understanding of both classical and modern mechanics. 0aMathematics. 0aDifferential geometry. 0aMathematical physics. 0aPhysics. 0aMechanics. 0aFluids. 0aContinuum mechanics.14aMathematics.24aDifferential Geometry.24aMechanics.24aMathematical Physics.24aFluid- and Aerodynamics.24aContinuum Mechanics and Mechanics of Materials.24aMathematical Methods in Physics.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780817683511 0aModeling and Simulation in Science, Engineering and Technology,x2164-367940uhttp://dx.doi.org/10.1007/978-0-8176-8352-8