Language:
English
繁體中文
Help
Login
Back
Switch To:
Labeled
|
MARC Mode
|
ISBD
Classical Newtonian Gravity = A Comp...
~
Capuzzo Dolcetta, Roberto A.
Classical Newtonian Gravity = A Comprehensive Introduction, with Examples and Exercises /
Record Type:
Language materials, printed : Monograph/item
Title/Author:
Classical Newtonian Gravity/ by Roberto A. Capuzzo Dolcetta.
Reminder of title:
A Comprehensive Introduction, with Examples and Exercises /
Author:
Capuzzo Dolcetta, Roberto A.
Description:
XVI, 176 p. 34 illus., 3 illus. in color.online resource. :
Contained By:
Springer Nature eBook
Subject:
Mechanics. -
Online resource:
https://doi.org/10.1007/978-3-030-25846-7
ISBN:
9783030258467
Classical Newtonian Gravity = A Comprehensive Introduction, with Examples and Exercises /
Capuzzo Dolcetta, Roberto A.
Classical Newtonian Gravity
A Comprehensive Introduction, with Examples and Exercises /[electronic resource] :by Roberto A. Capuzzo Dolcetta. - 1st ed. 2019. - XVI, 176 p. 34 illus., 3 illus. in color.online resource. - UNITEXT for Physics,2198-7882. - UNITEXT for Physics,.
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.
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.
ISBN: 9783030258467
Standard No.: 10.1007/978-3-030-25846-7doiSubjects--Topical Terms:
527684
Mechanics.
LC Class. No.: QC120-168.85
Dewey Class. No.: 531
Classical Newtonian Gravity = A Comprehensive Introduction, with Examples and Exercises /
LDR
:07024nam a22004215i 4500
001
1012653
003
DE-He213
005
20200702074143.0
007
cr nn 008mamaa
008
210106s2019 gw | s |||| 0|eng d
020
$a
9783030258467
$9
978-3-030-25846-7
024
7
$a
10.1007/978-3-030-25846-7
$2
doi
035
$a
978-3-030-25846-7
050
4
$a
QC120-168.85
050
4
$a
QA808.2
072
7
$a
PHD
$2
bicssc
072
7
$a
SCI041000
$2
bisacsh
072
7
$a
PHD
$2
thema
082
0 4
$a
531
$2
23
100
1
$a
Capuzzo Dolcetta, Roberto A.
$e
author.
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
1306912
245
1 0
$a
Classical Newtonian Gravity
$h
[electronic resource] :
$b
A Comprehensive Introduction, with Examples and Exercises /
$c
by Roberto A. Capuzzo Dolcetta.
250
$a
1st ed. 2019.
264
1
$a
Cham :
$b
Springer International Publishing :
$b
Imprint: Springer,
$c
2019.
300
$a
XVI, 176 p. 34 illus., 3 illus. in color.
$b
online resource.
336
$a
text
$b
txt
$2
rdacontent
337
$a
computer
$b
c
$2
rdamedia
338
$a
online resource
$b
cr
$2
rdacarrier
347
$a
text file
$b
PDF
$2
rda
490
1
$a
UNITEXT for Physics,
$x
2198-7882
505
0
$a
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.
520
$a
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.
650
0
$a
Mechanics.
$3
527684
650
0
$a
Space sciences.
$3
715034
650
0
$a
Potential theory (Mathematics).
$3
1255004
650
0
$a
Gravitation.
$3
591793
650
1 4
$a
Classical Mechanics.
$3
1140387
650
2 4
$a
Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics).
$3
1114976
650
2 4
$a
Potential Theory.
$3
672266
650
2 4
$a
Classical and Quantum Gravitation, Relativity Theory.
$3
769093
710
2
$a
SpringerLink (Online service)
$3
593884
773
0
$t
Springer Nature eBook
776
0 8
$i
Printed edition:
$z
9783030258450
776
0 8
$i
Printed edition:
$z
9783030258474
776
0 8
$i
Printed edition:
$z
9783030258481
830
0
$a
UNITEXT for Physics,
$x
2198-7882
$3
1254550
856
4 0
$u
https://doi.org/10.1007/978-3-030-25846-7
912
$a
ZDB-2-PHA
912
$a
ZDB-2-SXP
950
$a
Physics and Astronomy (SpringerNature-11651)
950
$a
Physics and Astronomy (R0) (SpringerNature-43715)
based on 0 review(s)
Multimedia
Reviews
Add a review
and share your thoughts with other readers
Export
pickup library
Processing
...
Change password
Login