LEADER 01729oam 2200457zu 450 001 996206428303316 005 20210807000336.0 035 $a(CKB)1000000000022858 035 $a(SSID)ssj0000394352 035 $a(PQKBManifestationID)12120548 035 $a(PQKBTitleCode)TC0000394352 035 $a(PQKBWorkID)10387915 035 $a(PQKB)11088564 035 $a(EXLCZ)991000000000022858 100 $a20160829d2003 uy 101 0 $aeng 181 $ctxt 182 $cc 183 $acr 200 10$aDIPED-2003 : proceedings of VIIIth International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory : Lviv, September 23-5, 2003 210 31$a[Place of publication not identified]$cPidstryhach Institute of Applied Problems of Mechanics and Mathematics NASU$d2003 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a966-02-2888-0 606 $aElectromagnetic waves$vCongresses 606 $aSound-waves$vCongresses 606 $aPhysics$2HILCC 606 $aElectricity & Magnetism$2HILCC 606 $aPhysical Sciences & Mathematics$2HILCC 615 0$aElectromagnetic waves 615 0$aSound-waves 615 7$aPhysics 615 7$aElectricity & Magnetism 615 7$aPhysical Sciences & Mathematics 676 $a537/.12 712 02$aInstytut prykladnykh problem mekhaniky i matematyky im. 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DEI LINCEI E CORSINIANA$bRM0418 899 $aBiblioteca umanistica Giorgio Aprea$bFR0017 $eN 912 $aLO11084590 950 0$aBiblioteca umanistica Giorgio Aprea$d 52SALA BRAGAS.S.L. 62.22$e 52ATE0000031275 VMN RS $fA $h20161004$i20161004 977 $a 01$a 06$a 07$a 08$a 10$a 52 996 $aBible hébraique$9265767 997 $aUNICAS LEADER 08114nam 22006735 450 001 9910349501303321 005 20251116220158.0 010 $a9783030258467 010 $a3030258467 024 7 $a10.1007/978-3-030-25846-7 035 $a(CKB)4100000009362514 035 $a(DE-He213)978-3-030-25846-7 035 $a(MiAaPQ)EBC5922390 035 $a(PPN)269147667 035 $a(MiAaPQ)EBC31850086 035 $a(Au-PeEL)EBL31850086 035 $a(EXLCZ)994100000009362514 100 $a20190923d2019 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aClassical Newtonian Gravity $eA Comprehensive Introduction, with Examples and Exercises /$fby Roberto A. Capuzzo Dolcetta 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (XVI, 176 p. 34 illus., 3 illus. in color.) 225 1 $aUNITEXT for Physics,$x2198-7882 311 08$a9783030258450 311 08$a3030258459 327 $aChapter 1 -- Elements of Vector Calculus -- 1.1 Vector Functions of Real Variables -- 1.2 Limits of vector Functions -- 1.3 Derivatives of Vector Functions -- 1.3.1 Geometrie Interpretation -- 1.4 Integrals of Vector Functions -- 1.5 The Formal Operator Nabla, ? -- 1.5.1 ? in Polar Coordinates -- 1.5.2 ? in Cylindrical Coordinates -- 1.6 The Divergence Operator -- 1.7 The Curl Operator -- 1.8 Divergence and Curl by Means of ? -- 1.8.1 Spherical Polar Coordinates -- 1.8.2 Cylindrieal Coordinates -- 1.9 Vector Fields -- 1.9.1 Field Lines -- 1.10 Divergence Theorem -- 1.10.1 Velocity Fields -- 1.10.2 Continuity Equation -- 1.10.3 Field Lines of Solenoidal Fields -- Chapter 2 Potential Theory -- Discrete mass distributions -- 2.1 Single particle gravitational potential -- 2.2 The gravitating N body case -- 2.3 Mechanical Energy of the N bodies -- 2.4 The Scalar Virial Theorem -- 2.4.1 Consequenees of the Virial Theorem -- 2.5 Newtonian Gravitational Force and Potential -- 2.6 Gauss Theorem -- 2.7 Gravitational Potential Energy -- 2.8 Newton?s Theorems -- Chapter 3 -- Central Force Fields -- 3.1 Force and Potential of a Spherical Mass Distribution -- 3.2 Circular orbits -- 3.2 Potential of a Homogeneous Sphere -- 3.3.1 Quality of Motion -- 3.3.2 Particle Trajectories -- 3.4 Periods of Oscillations -- 3.4.1 Radial and Azimuthal Oscillations -- 3.4.2 Radial Oscillations in a Homogeneous Sphere -- 3.4.3 Radial Oscillations in a Point Mass Potential -- 3.5 The Isochrone Potential -- 3.6 The Inverse Problem in Spherical Distributions -- Chapter 4 -- Potential Series Developments -- 4.1 Fundamental Solution of Laplace'sChapter 1 -- Elements of Vector Calculus -- 1.1 Vector Functions of Real Variables -- 1.2 Limits of vector Functions -- 1.3 Derivatives of Vector Functions -- 1.3.1 Geometrie Interpretation -- 1.4 Integrals of Vector Functions -- 1.5 The Formal Operator Nabla, ? -- 1.5.1 ? in Polar Coordinates -- 1.5.2 ? in Cylindrical Coordinates -- 1.6 The Divergence Operator -- 1.7 The Curl Operator -- 1.8 Divergence and Curl by Means of ? -- 1.8.1 Spherical Polar Coordinates -- 1.8.2 Cylindrieal Coordinates -- 1.9 Vector Fields -- 1.9.1 Field Lines -- 1.10 Divergence Theorem -- 1.10.1 Velocity Fields -- 1.10.2 Continuity Equation -- 1.10.3 Field Lines of Solenoidal Fields -- Chapter 2 Potential Theory -- Discrete mass distributions -- 2.1 Single particle gravitational potential -- 2.2 The gravitating N body case -- 2.3 Mechanical Energy of the N bodies -- 2.4 The Scalar Virial Theorem -- 2.4.1 Consequenees of the Virial Theorem -- 2.5 Newtonian Gravitational Force and Potential -- 2.6 Gauss Theorem -- 2.7 Gravitational Potential Energy -- 2.8 Newton?s Theorems -- Chapter 3 -- Central Force Fields -- 3.1 Force and Potential of a Spherical Mass Distribution -- 3.2 Circular orbits -- 3.2 Potential of a Homogeneous Sphere -- 3.3.1 Quality of Motion -- 3.3.2 Particle Trajectories -- 3.4 Periods of Oscillations -- 3.4.1 Radial and Azimuthal Oscillations -- 3.4.2 Radial Oscillations in a Homogeneous Sphere -- 3.4.3 Radial Oscillations in a Point Mass Potential -- 3.5 The Isochrone Potential -- 3.6 The Inverse Problem in Spherical Distributions -- Chapter 4 -- Potential Series Developments -- 4.1 Fundamental Solution of Laplace's Equation -- 4.2 Harmonic Functions -- 4.3 Legendre's Polynomials -- 4.4 Recursive Relations -- 4.4.1 First Recursive Relation -- 4.4.2 Second Recursive Relation -- 4.5 Legendre Differential Equation -- 4.6 Orthogonality of Legendre's Polynomials -- 4.7 Development in Series of Legendre's Polynomials -- 4.8 Rodrigues Formula Chapter 5 -- Harmonic and Homogeneous Polynomials -- 5.1 Spherical Harmonics -- 5.2 Solution of the Differential equations for Sm(?, ?) -- 5.3 The Solution in ? -- 5.4 A note on the Associated Legendre Differential Equation -- 5.5 Zonal, Sectorial and Tesseral Spherical Harmonics -- 5.5.1Orthogonality Properties -- Chapter 6 -- Series of Spherical Harmonics -- 6.1 Potential Developments Out of a Mass Distribution -- 6.2 The External Earth Potential -- 6.3 Exercises. 330 $aThis textbook offers a readily comprehensible introduction to classical Newtonian gravitation, which is fundamental for an understanding of classical mechanics and is particularly relevant to Astrophysics. The opening chapter recalls essential elements of vectorial calculus, especially to provide the formalism used in subsequent chapters. In chapter two Classical Newtonian gravity theory for one point mass and for a generic number N of point masses is then presented and discussed. The theory for point masses is naturally extended to the continuous case. The third chapter addresses the paradigmatic case of spherical symmetry in the mass density distribution (central force), with introduction of the useful tool of qualitative treatment of motion. Subsequent chapters discuss the general case of non-symmetric mass density distribution and develop classical potential theory, with elements of harmonic theory, which is essential to understand the potential development in series of the gravitational potential, the subject of the fourth chapter. Finally, in the last chapter the specific case of motion of a satellite around the earth is considered. Examples and exercises are presented throughout the book to clarify aspects of the theory. The book is aimed at those who wish to progress further beyond an initial bachelor degree, onward to a master degree, and a PhD. It is also a valuable resource for postgraduates and active researchers in the field. 410 0$aUNITEXT for Physics,$x2198-7882 606 $aMechanics 606 $aSpace sciences 606 $aPotential theory (Mathematics) 606 $aGravitation 606 $aClassical Mechanics$3https://scigraph.springernature.com/ontologies/product-market-codes/P21018 606 $aSpace Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics)$3https://scigraph.springernature.com/ontologies/product-market-codes/P22030 606 $aPotential Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12163 606 $aClassical and Quantum Gravitation, Relativity Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P19070 615 0$aMechanics. 615 0$aSpace sciences. 615 0$aPotential theory (Mathematics) 615 0$aGravitation. 615 14$aClassical Mechanics. 615 24$aSpace Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics). 615 24$aPotential Theory. 615 24$aClassical and Quantum Gravitation, Relativity Theory. 676 $a530.092 676 $a526.7 700 $aCapuzzo-Dolcetta$b Roberto$4aut$4http://id.loc.gov/vocabulary/relators/aut$01776487 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910349501303321 996 $aClassical Newtonian Gravity$94294481 997 $aUNINA