Classical Newtonian Gravity A Comprehensive Introduction, with Examples and Exercises /

• Κύριος συγγραφέας: Capuzzo Dolcetta, Roberto A. (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Έκδοση: 1st ed. 2019.
• Σειρά: UNITEXT for Physics,
• Θέματα: Mechanics.; Space sciences.; Potential theory (Mathematics).; Gravitation.; Classical Mechanics.; Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics).; Potential Theory.; Classical and Quantum Gravitation, Relativity Theory.

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 th...

Πίνακας περιεχομένων:

• 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, ϕ)
• 5.3 The Solution in ϕ
• 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.