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Shapes and Dynamics of Granular Minor Planets: The Dynamics of Deformable Bodies Applied to Granular Objects in the Solar System 1st ed. 2017 [Kõva köide]

  • Formaat: Hardback, 354 pages, kõrgus x laius: 235x155 mm, kaal: 887 g, 25 Illustrations, color; 91 Illustrations, black and white; XX, 354 p. 116 illus., 25 illus. in color., 1 Hardback
  • Sari: Advances in Geophysical and Environmental Mechanics and Mathematics
  • Ilmumisaeg: 15-Dec-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 331940489X
  • ISBN-13: 9783319404899
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Shapes and Dynamics of Granular Minor Planets: The Dynamics of Deformable Bodies Applied to Granular Objects in the Solar System 1st ed. 2017Suurem pilt
  • Formaat: Hardback, 354 pages, kõrgus x laius: 235x155 mm, kaal: 887 g, 25 Illustrations, color; 91 Illustrations, black and white; XX, 354 p. 116 illus., 25 illus. in color., 1 Hardback
  • Sari: Advances in Geophysical and Environmental Mechanics and Mathematics
  • Ilmumisaeg: 15-Dec-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 331940489X
  • ISBN-13: 9783319404899
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783319404899.html
Märksõnad:
This book develops a general approach that can be systematically refined to investigate the statics and dynamics of deformable solid bodies. These methods are then employed to small bodies in the Solar System. With several space missions underway and more being planned, interest in our immediate neighbourhood is growing. In this spirit, this book investigates various phenomena encountered in planetary science, including disruptions during planetary fly-bys, equilibrium shapes and stability of small rubble bodies, and spin-driven shape changes.The flexible procedure proposed here will help readers gain valuable insights into the mechanics of solar system bodies, while at the same time complementing numerical investigations. The technique itself is built upon the virial method successfully employed by Chandrasekhar (1969) to study the equilibrium shapes of spinning fluid objects. However, here Chandrasekhar"s approach is modified in order to study more complex dynamical situations

and include objects of different rheologies, e.g., granular aggregates, or "rubble piles". The book is largely self-contained, though some basic familiarity with continuum mechanics will be beneficial.

1. Introduction 2. Dynamics 3. Bodies in Space 4. Celestial mechanics
Part I Toolbox
1 Mathematical Preliminaries
3(12)
1.1 Coordinate Systems
3(1)
1.2 Vectors
3(1)
1.3 Tensors
4(6)
1.3.1 Second-Order Tensors
4(5)
1.3.2 Third- and Fourth-Order Tensors
9(1)
1.4 Coordinate Transformation
10(1)
1.5 Calculus
11(4)
1.5.1 Gradient and Divergence. Taylor's Theorem
11(1)
1.5.2 The Divergence Theorem
12(1)
1.5.3 Time-Varying Fields
12(1)
References
13(2)
2 Continuum Mechanics
15(36)
2.1 Introduction
15(1)
2.2 Motion in a Rotating Coordinate System
16(2)
2.2.1 Vectors and Tensors
16(1)
2.2.2 Velocity and Acceleration
17(1)
2.3 Kinematics
18(2)
2.4 Simple Motions
20(3)
2.4.1 Example 1: Pure Rotation
20(1)
2.4.2 Example 2: General Rigid Body Motion
21(1)
2.4.3 Example 3: Homogeneous Motion
22(1)
2.4.4 Example 4: Affine Motion
22(1)
2.5 Local Motion
23(6)
2.5.1 Strain. Surface Change. Volume Change
24(1)
2.5.2 Rate of Local Motion
25(2)
2.5.3 Transport Theorem. Mass Balance
27(2)
2.6 Further Analysis of Simple Motions
29(3)
2.6.1 Example 3: Homogeneous Motion
29(2)
2.6.2 Example 4: Affine Motion
31(1)
2.7 Stress
32(1)
2.8 Moments of the Stress Tensor
33(3)
2.9 Power Balance
36(1)
2.10 Constitutive Laws
37(14)
2.10.1 Rigid-Perfectly Plastic Materials
38(6)
2.10.2 Material Parameters
44(4)
References
48(3)
3 Affine Dynamics
51(24)
3.1 Introduction
51(2)
3.2 Governing Equations: Structural Motion
53(3)
3.2.1 Statics
55(1)
3.3 Moment Tensors
56(6)
3.3.1 Gravitational-Moment Tensor
57(2)
3.3.2 Tidal-Moment Tensor
59(3)
3.4 Governing Equations: Orbital Motion
62(5)
3.4.1 Circular Tidally-Locked Orbits
64(3)
3.5 Conservation Laws
67(8)
3.5.1 Angular Momentum Balance
67(1)
3.5.2 Power Balance
68(2)
3.5.3 Total Energy of a Deformable Gravitating Ellipsoid
70(1)
References
71(4)
Part II Equilibrium
4 Asteroids
75(20)
4.1 Introduction
75(1)
4.2 Governing Equations
76(3)
4.2.1 Average Stresses
76(2)
4.2.2 Non-dimensionalization
78(1)
4.2.3 Coordinate System
78(1)
4.3 Equilibrium Landscape
79(7)
4.3.1 Oblate Asteroids
83(1)
4.3.2 Prolate Asteroids
84(1)
4.3.3 Triaxial Asteroids
84(2)
4.4 Discussion
86(2)
4.5 Applications
88(4)
4.5.1 Material Parameters
88(1)
4.5.2 Near-Earth Asteroid Data
88(1)
4.5.3 Equilibrium Shapes
89(3)
4.6 Summary
92(3)
References
92(3)
5 Satellites
95(34)
5.1 Introduction
95(1)
5.2 Governing Equations
96(5)
5.2.1 Average Stress
97(1)
5.2.2 Orbital Motion
98(1)
5.2.3 Non-dimensionalization
98(2)
5.2.4 Coordinate System
100(1)
5.3 Example: Satellites of Oblate Primaries
101(9)
5.3.1 Bp(0) and Bp(1)
102(1)
5.3.2 The Orbital Rate ωE11
103(1)
5.3.3 Equilibrium Landscape
103(7)
5.4 Application: The Roche Problem
110(6)
5.4.1 Material Parameters
111(1)
5.4.2 Moons of Mars
112(1)
5.4.3 Alternate Yield Criteria and Previous Work
113(3)
5.5 Application: Satellites of the Giant Planets
116(9)
5.5.1 Satellite Data
118(2)
5.5.2 Locations
120(1)
5.5.3 Discussion
120(5)
5.6 Summary
125(4)
References
126(3)
6 Binaries
129(34)
6.1 Introduction
129(1)
6.2 Governing Equation
130(5)
6.2.1 Average Stresses
131(1)
6.2.2 Orbital Motion
132(1)
6.2.3 Non-dimensionalization
132(2)
6.2.4 Coordinate Systems
134(1)
6.3 Example: Prolate Binary System
135(2)
6.3.1 B(0), B(1) and B(2)
136(1)
6.3.2 The Orbital Rate ωB
137(1)
6.4 Equilibrium Landscape
137(8)
6.5 Example: Fluid Binaries and the Roche Binary Approximation
145(3)
6.6 Application: Binary Asteroids
148(10)
6.6.1 216 Kleopatra
151(3)
6.6.2 25143 Itokawa
154(1)
6.6.3 624 Hektor
155(2)
6.6.4 90 Antiope
157(1)
6.7 Summary
158(5)
References
158(5)
Part III Stability
7 Granular Materials
163(16)
7.1 Introduction
163(1)
7.2 Stability
164(15)
7.2.1 Coordinate System
165(2)
7.2.2 Energy Criterion
167(5)
7.2.3 Compatibility and Normality
172(1)
7.2.4 Stability at First-Order
173(2)
7.2.5 Stability at Second-Order
175(1)
7.2.6 Stability to Finite Perturbations
175(2)
References
177(2)
8 Asteroids
179(28)
8.1 Introduction
179(1)
8.2 Asteroid Dynamics
180(2)
8.3 Stability
182(5)
8.3.1 Coordinate System
182(3)
8.3.2 Energy Criterion
185(2)
8.4 Example: Rubble-Pile Asteroids
187(9)
8.4.1 Compatible Perturbations
189(1)
8.4.2 Local Stability
190(3)
8.4.3 Stability to Finite Perturbations
193(3)
8.5 Application: Near-Earth Asteroids
196(8)
8.5.1 Near-Earth Asteroid Data
196(2)
8.5.2 Local Stability
198(2)
8.5.3 Planetary Encounters
200(4)
8.6 Summary
204(3)
References
205(2)
9 Satellites
207(30)
9.1 Introduction
207(1)
9.2 Satellite Dynamics
208(3)
9.2.1 Structural Deformation
208(2)
9.2.2 Orbital Motion
210(1)
9.3 Stability
211(7)
9.3.1 Coordinate System
211(2)
9.3.2 Energy Criterion
213(5)
9.4 Example: Rubble-Pile Planetary Satellites
218(10)
9.4.1 Orbital Stability
218(3)
9.4.2 Structural Stability
221(1)
9.4.3 Local Stability
222(3)
9.4.4 Stability to Finite Structural Perturbations
225(3)
9.5 Application: Planetary Satellites
228(7)
9.5.1 Local Stability
228(5)
9.5.2 Stability to Finite Structural Perturbations
233(2)
9.6 Summary
235(2)
References
236(1)
10 Binaries
237(48)
10.1 Introduction
237(1)
10.2 Binary Dynamics
238(4)
10.2.1 Structural Motion
239(2)
10.2.2 Orbital Motion
241(1)
10.3 Stability
242(8)
10.3.1 Coordinate System
243(2)
10.3.2 Admissible Perturbations
245(2)
10.3.3 Energy Criterion
247(3)
10.4 Components
250(1)
10.5 Example: Planar Binary with Near-Spherical, Rigid Members
250(2)
10.6 Example: Rigid Binaries
252(9)
10.6.1 Orbital Kinetic Energy
254(1)
10.6.2 Structural Kinetic Energy
255(1)
10.6.3 Perturbations
256(1)
10.6.4 Stability
256(5)
10.7 Example: Rubble-Pile Binaries
261(11)
10.7.1 Orbital Kinetic Energy
261(2)
10.7.2 Structural Kinetic Energy
263(1)
10.7.3 Perturbations
264(1)
10.7.4 Local Stability
265(5)
10.7.5 Stability to Finite Structural Perturbations
270(2)
10.8 Application: Near-Earth Binaries
272(9)
10.8.1 216 Kleopatra
272(3)
10.8.2 25143 Itokawa
275(1)
10.8.3 624 Hektor
276(1)
10.8.4 90 Antiope
276(1)
10.8.5 Stability to Finite Structural Perturbations
277(4)
10.9 Summary
281(4)
References
281(4)
Part IV Dynamics
11 Formation
285(22)
11.1 Introduction
285(1)
11.2 Governing Equations
285(5)
11.2.1 Non-dimensionalization
288(1)
11.2.2 Components
289(1)
11.3 Example: Prolate Asteroids
290(15)
11.3.1 Switching States
291(1)
11.3.2 Numerical Algorithm
292(1)
11.3.3 Application: Equilibrium Shapes
293(5)
11.3.4 Discussion: Dynamics of a Homogeneously Deforming Rigid---Plastic Ellipsoid
298(7)
11.4 Summary
305(2)
References
305(2)
12 Tidal Flybys
307(30)
12.1 Introduction
307(1)
12.2 Setup
308(2)
12.3 Governing Equations
310(2)
12.4 Material Behavior
312(4)
12.4.1 A Kinetic Theory Based Model for Loose Granular Aggregates
312(3)
12.4.2 Transition Criterion
315(1)
12.5 Results
316(18)
12.5.1 Outcomes with the Tensile Criterion
317(2)
12.5.2 The Roche Limit
319(2)
12.5.3 Further Analysis of Flybys
321(7)
12.5.4 Outcomes with the Mohr-Coulomb Criterion
328(1)
12.5.5 The Effect of Rotation Direction
329(4)
12.5.6 Different Initial Rotation Rates
333(1)
12.6 Summary
334(3)
References
334(3)
Appendix A Rate of Change of the Gravitational Shape Tensor 337(4)
Appendix B The Tidal Shape Tensor 341(4)
Appendix C Rate of Change of the Tidal Shape Tensor 345(4)
Index 349