Classical Newtonian Gravity / Capuzzo Dolcetta, Roberto A.  

Público ISBD Ningún comentario para este registro. Título : Classical Newtonian Gravity : A Comprehensive Introduction, with Examples and Exercises Tipo de documento: documento electrónico Autores: Capuzzo Dolcetta, Roberto A., Mención de edición: 1 ed. Editorial: [s.l.] : Springer Fecha de publicación: 2019 Número de páginas: XVI, 176 p. 34 ilustraciones, 3 ilustraciones en color. ISBN/ISSN/DL: 978-3-030-25846-7 Nota general: Libro disponible en la plataforma SpringerLink. Descarga y lectura en formatos PDF, HTML y ePub. Descarga completa o por capítulos. Idioma : Inglés (eng) Palabras clave: Mecánica  Sistema solar  Teoría potencial (Matemáticas)  Gravitación  Mecanica clasica  Física espacial  Teoría potencial  Gravedad clásica y cuántica Clasificación: 531 Resumen: Este libro de texto ofrece una introducción fácilmente comprensible a la gravitación newtoniana clásica, que es fundamental para la comprensión de la mecánica clásica y es particularmente relevante para la Astrofísica. El capítulo inicial recuerda elementos esenciales del cálculo vectorial, especialmente para proporcionar el formalismo utilizado en los capítulos siguientes. En el capítulo dos, se presenta y analiza la teoría clásica de la gravedad newtoniana para una masa puntual y para un número genérico N de masas puntuales. La teoría de masas puntuales se extiende naturalmente al caso continuo. El tercer capítulo aborda el caso paradigmático de la simetría esférica en la distribución de densidad de masa (fuerza central), con la introducción de la útil herramienta de tratamiento cualitativo del movimiento. Los capítulos siguientes discuten el caso general de la distribución asimétrica de la densidad de masa y desarrollan la teoría del potencial clásica, con elementos de la teoría armónica, que es esencial para comprender el desarrollo potencial en serie del potencial gravitacional, tema del cuarto capítulo. Finalmente, en el último capítulo se considera el caso específico del movimiento de un satélite alrededor de la Tierra. A lo largo del libro se presentan ejemplos y ejercicios para aclarar aspectos de la teoría. El libro está dirigido a aquellos que desean avanzar más allá de una licenciatura inicial, hacia una maestría y un doctorado. También es un recurso valioso para posgraduados e investigadores activos en el campo. Nota de contenido: Chapter 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(θ, Ï•) -- 5.3 The Solution in Ï• -- 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. Tipo de medio : Computadora Summary : This 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. Enlace de acceso : https://link-springer-com.biblioproxy.umanizales.edu.co/referencework/10.1007/97 [...] Classical Newtonian Gravity : A Comprehensive Introduction, with Examples and Exercises [documento electrónico] / Capuzzo Dolcetta, Roberto A.,  . -  1 ed.  . - [s.l.] : Springer, 2019 . - XVI, 176 p. 34 ilustraciones, 3 ilustraciones en color. ISBN : 978-3-030-25846-7 Libro disponible en la plataforma SpringerLink. Descarga y lectura en formatos PDF, HTML y ePub. Descarga completa o por capítulos. Idioma : Inglés (eng) Palabras clave: Mecánica  Sistema solar  Teoría potencial (Matemáticas)  Gravitación  Mecanica clasica  Física espacial  Teoría potencial  Gravedad clásica y cuántica Clasificación: 531 Resumen: Este libro de texto ofrece una introducción fácilmente comprensible a la gravitación newtoniana clásica, que es fundamental para la comprensión de la mecánica clásica y es particularmente relevante para la Astrofísica. El capítulo inicial recuerda elementos esenciales del cálculo vectorial, especialmente para proporcionar el formalismo utilizado en los capítulos siguientes. En el capítulo dos, se presenta y analiza la teoría clásica de la gravedad newtoniana para una masa puntual y para un número genérico N de masas puntuales. La teoría de masas puntuales se extiende naturalmente al caso continuo. El tercer capítulo aborda el caso paradigmático de la simetría esférica en la distribución de densidad de masa (fuerza central), con la introducción de la útil herramienta de tratamiento cualitativo del movimiento. Los capítulos siguientes discuten el caso general de la distribución asimétrica de la densidad de masa y desarrollan la teoría del potencial clásica, con elementos de la teoría armónica, que es esencial para comprender el desarrollo potencial en serie del potencial gravitacional, tema del cuarto capítulo. Finalmente, en el último capítulo se considera el caso específico del movimiento de un satélite alrededor de la Tierra. A lo largo del libro se presentan ejemplos y ejercicios para aclarar aspectos de la teoría. El libro está dirigido a aquellos que desean avanzar más allá de una licenciatura inicial, hacia una maestría y un doctorado. También es un recurso valioso para posgraduados e investigadores activos en el campo. Nota de contenido: Chapter 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(θ, Ï•) -- 5.3 The Solution in Ï• -- 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. Tipo de medio : Computadora Summary : This 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. Enlace de acceso : https://link-springer-com.biblioproxy.umanizales.edu.co/referencework/10.1007/97 [...]

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