Classical Newtonian gravity : a comprehensive introduction, with examples and exercises /: a comprehensive introduction, with examples and exercises. ([2019])
- Record Type:
- Book
- Title:
- Classical Newtonian gravity : a comprehensive introduction, with examples and exercises /: a comprehensive introduction, with examples and exercises. ([2019])
- Main Title:
- Classical Newtonian gravity : a comprehensive introduction, with examples and exercises
- Further Information:
- Note: Roberto A. Capuzzo Dolcetta.
- Authors:
- Capuzzo-Dolcetta, Roberto
- Contents:
- 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 SphericalChapter 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, 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. … (more)
- Publisher Details:
- Cham, Switzerland : Springer
- Publication Date:
- 2019
- Extent:
- 1 online resource
- Subjects:
- 526.7
Gravity
Electronic books - Languages:
- English
- ISBNs:
- 9783030258467
3030258467 - Related ISBNs:
- 3030258459
9783030258450 - Notes:
- Note: Includes bibliographical references.
Note: Description based on online resource; title from digital title page (viewed on October 03, 2019). - Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
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- British Library HMNTS - ELD.DS.458469
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