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Contents
| 3 | |
| 8 | |
References | 19 |
Problems | 20 |
Newtonian Mechanics | 27 |
23 Single Particle Dynamics | 31 |
24 Dynamics of a System of Particles | 43 |
25 Dynamics of a Continuous System | 53 |
Problems | 374 |
Celestial Mechanics | 379 |
Classical TwoBody Problem | 381 |
92 Geometry of Conic Sections | 382 |
93 Relative TwoBody Equations of Motion | 390 |
94 Fundamental Integrals | 392 |
95 Classical Solutions | 404 |
References | 420 |
26 Rocket Problem | 58 |
References | 63 |
Rigid Body Kinematics | 71 |
32 Direction Cosine Matrix | 72 |
33 Euler Angles | 78 |
34 Principal Rotation Vector | 87 |
35 Euler Parameters | 95 |
36 Classical Rodrigues Parameters | 102 |
37 Modified Rodrigues Parameters | 107 |
38 Other Attitude Parameters | 115 |
39 Homogeneous Transformations | 119 |
References | 122 |
Problems | 123 |
Eulerian Mechanics | 127 |
43 TorqueFree Rigid Body Rotation | 142 |
44 Momentum Exchange Devices | 151 |
45 Gravity Gradient Satellite | 160 |
References | 170 |
Problems | 171 |
Generalized Methods of Analytical Dynamics | 177 |
53 DAlemberts Principle | 180 |
54 Lagrangian Dynamics | 204 |
References | 231 |
Variational Methods in Analytical Dynamics | 237 |
63 Hamiltons Variational Principles | 241 |
64 Hamiltons Principal Function | 245 |
65 Some Classical Applications of Hamiltons Principle to Distributed Parameter Systems | 247 |
66 Explicit Generalizations of Lagranges Equations for Hybrid Coordinate Systems | 254 |
References | 261 |
Hamiltons Generalized Formulations of Analytical Dynamics | 265 |
73 Ignorable Coordinates | 270 |
74 Relationship of Hamiltonian Function to WorkEnergy Integral | 271 |
75 Hamiltons Canonical Equations | 276 |
76 Poissons Brackets | 280 |
77 Canonical Coordinate Transformations | 283 |
78 Perfect Differential Criterion for Canonical Transformations | 287 |
79 Transformation Jacobian Perspective on Canonical Transformations | 290 |
References | 292 |
Nonlinear Spacecraft Stability and Control | 295 |
83 Generating Lyapunov Functions | 310 |
84 Nonlinear Feedback Control Laws | 325 |
85 Lyapunov Optimal Control Laws | 339 |
86 Linear ClosedLoop Dynamics | 345 |
87 Reaction Wheel Control Devices | 351 |
88 Variable Speed Control Moment Gyroscopes | 353 |
References | 372 |
Problems | 421 |
Restricted ThreeBody Problem | 423 |
103 Circular Restricted ThreeBody Problem | 438 |
104 Periodic Stationary Orbits | 458 |
105 Disturbing Function | 460 |
References | 463 |
Gravitational Potential Field Models | 465 |
112 Gravitational Potential of Finite Bodies | 466 |
113 MacCullaghs Approximation | 469 |
114 Spherical Harmonic Gravity Potential | 472 |
115 Multibody Gravitational Acceleration | 483 |
116 Spheres of Gravitational Influence | 485 |
References | 488 |
Perturbation Methods | 489 |
122 Enckes Method | 490 |
123 Variation of Parameters | 492 |
124 State Transition and Sensitivity Matrix | 525 |
References | 540 |
Problems | 541 |
Transfer Orbits | 545 |
133 Hohmann Transfer Orbit | 549 |
134 Lamberts Problem | 554 |
135 Rotating the Orbit Plane | 563 |
136 PatchedConic Orbit Solution | 568 |
References | 589 |
Spacecraft Formation Flying | 593 |
142 General Relative Orbit Description | 594 |
143 Cartesian Coordinate Description | 596 |
144 Orbit Element Difference Description | 604 |
145 Relative Motion State Transition Matrix | 613 |
146 Linearized Relative Orbit Motion | 618 |
147 J2ln variant Relative Orbits | 628 |
148 Relative Orbit Control Methods | 649 |
References | 669 |
| 671 | |
Transport Theorem Derivation Using Linear Algebra | 675 |
Various Euler Angle Transformations | 679 |
MRP Identity Proof | 683 |
Conic Section Transformations | 685 |
MATLAB MFiles | 689 |
FirstOrder Mapping Between Mean and Osculating Orbit Elements | 693 |
Direct Linear Mapping Between Cartesian Hill Frame Coordinates and Orbit Element Differences | 697 |
Hamel Coefficients for the Rotational Motion of a Rigid Body | 699 |
| 707 | |
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Common terms and phrases
angular momentum angular momentum vector angular velocity angular velocity vector argument of perigee Assume asymptotic stability asymptotically center of mass chief orbit compute constant constraint coordinate system defined direction cosine matrix Earth eccentricity equation in Eq equations of motion error Euler angles Euler parameters Example feedback control law feedback gain force given gravitational illustrated inertia matrix inertial initial velocity integral inverse Keplerian kinetic energy Lagrange Lagrange's equations linear Lyapunov function mean anomaly mean orbit element nonlinear Note null motion orbit element differences orbit elements orbit plane orbit radius osculating osculating orbit partial derivative particle perturbations planet position vector principal rotation problem reference frame relative orbit rigid body satellite scalar semimajor axis shown in Fig singular solution solve spacecraft stability steering law Substituting Eq three-body tion trajectory transfer orbit transformation true anomaly two-body variation vector components VSCMG written zero
Popular passages
Page 670 - CLOHESSY, WH and WILTSHIRE, RS, "Terminal Guidance System for Satellite Rendezvous", Journal of the Aerospace Sciences, Vol. 27, No. 9, Sept.
Page 671 - Asymptotic Stability Theorem for Autonomous Systems," Journal of Guidance, Control, and Dynamics, Vol. 16, Sept.Oct. 1993, pp. 961-963.
References to this book
Bibliographic information
| Title | Analytical Mechanics of Space Systems AIAA education series Analytical Mechanics of Space Systems, Hanspeter Schaub |
| Authors | Hanspeter Schaub, John L. Junkins |
| Publisher | AIAA, 2003 |
| ISBN | 1600860273, 9781600860270 |
| Length | 716 pages |
| Export Citation | BiBTeX EndNote RefMan |