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Author: Victor R. Bond
Publisher: Princeton University Press
ISBN: 0691044597
Category : Science
Languages : en
Pages : 263
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Book Description
Newton's laws of motion and his universal law of gravitation described mathematically the motion of two bodies undergoing mutual gravitational attraction. However, it is impossible to solve analytically the equation of motion for three gravitationally interacting bodies. This book discusses some techniques used to obtain numerical solutions of the equations of motion for planets and satellites, which are of fundamental importance to solar-system dynamicists and to those involved in planning the orbits of artificial satellites. The first part introduces the classical two-body problem and solves it by rigorously developing the six integrals of the motion, starting from Newton's three laws of motion and his law of gravitation and then using vector algebra to develop the integrals. The various forms of the solution flow naturally from the integrals. In the second part, several modern perturbation techniques are developed and applied to cases of practical importance. For example, the perturbed two-body problem for an oblate planet or for a nonsymmetric rotating planet is considered, as is the effect of drag on a satellite. The two-body problem is regularized, and the nonlinear differential equation is thereby transformed to a linear one by further embedding several of the integrals. Finally, a brief sketch of numerical methods is given, as the perturbation equations must be solved by numerical rather than by analytical methods.
Author: Victor R. Bond
Publisher: Princeton University Press
ISBN: 0691044597
Category : Science
Languages : en
Pages : 263
Get Book
Book Description
Newton's laws of motion and his universal law of gravitation described mathematically the motion of two bodies undergoing mutual gravitational attraction. However, it is impossible to solve analytically the equation of motion for three gravitationally interacting bodies. This book discusses some techniques used to obtain numerical solutions of the equations of motion for planets and satellites, which are of fundamental importance to solar-system dynamicists and to those involved in planning the orbits of artificial satellites. The first part introduces the classical two-body problem and solves it by rigorously developing the six integrals of the motion, starting from Newton's three laws of motion and his law of gravitation and then using vector algebra to develop the integrals. The various forms of the solution flow naturally from the integrals. In the second part, several modern perturbation techniques are developed and applied to cases of practical importance. For example, the perturbed two-body problem for an oblate planet or for a nonsymmetric rotating planet is considered, as is the effect of drag on a satellite. The two-body problem is regularized, and the nonlinear differential equation is thereby transformed to a linear one by further embedding several of the integrals. Finally, a brief sketch of numerical methods is given, as the perturbation equations must be solved by numerical rather than by analytical methods.
Author: William E. Wiesel
Publisher:
ISBN: 9780974827216
Category : Astrodynamics
Languages : en
Pages : 229
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Book Description
Beginning from an understanding of Hamiltonian dynamics, Modern Astrodynamics blends the modern methods of dynamical system theory with the classical perturbation methods. Emphasizing earth satellite motion, the work also explores planetary motion. The text concludes with nonlinear resonance and relative motion of satellites. A Windows PC program disk suppliments the text.
Author:
Publisher: Elsevier
ISBN: 9780080464916
Category : Science
Languages : en
Pages : 336
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Book Description
In recent years, an unprecedented interest in novel and revolutionary space missions has risen out of the advanced NASA and ESA programs. Astrophysicists, astronomers, space systems engineers, mathematicians and scientists have been cooperating to implement novel and ground-breaking space missions. Recent progress in mathematical dynamics has enabled development of specialised spacecraft orbits and propulsion systems. Recently, the concept of flying spacecraft in formation has gained a lot of interest within the community. These progresses constitute the background to a significant renaissance of research dealing with astrodynamics and its applications. Modern Astrodynamics is designed as a stepping stone for the exposition of modern astrodynamics to students, researchers, engineers and scientists. This volume will present the main constituents of the astrodynamical science in an elaborate, comprehensive and rigorous manner. Although the volume will contain a few distinct chapters, it will render a coherent portrayal of astrodynamics. Encompasses the main constituents of the astrodynamical sciences in an elaborate, comprehensive and rigorous manner Presents recent astrodynamical advances and describes the challenges ahead The first volume of a series designed to give scientists and engineers worldwide an opportunity to publish their works in this multi-disciplinary field
Author: Victor R. Bond
Publisher: Princeton University Press
ISBN: 0691223904
Category : Science
Languages : en
Pages : 266
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Book Description
Newton's laws of motion and his universal law of gravitation described mathematically the motion of two bodies undergoing mutual gravitational attraction. However, it is impossible to solve analytically the equation of motion for three gravitationally interacting bodies. This book discusses some techniques used to obtain numerical solutions of the equations of motion for planets and satellites, which are of fundamental importance to solar-system dynamicists and to those involved in planning the orbits of artificial satellites. The first part introduces the classical two-body problem and solves it by rigorously developing the six integrals of the motion, starting from Newton's three laws of motion and his law of gravitation and then using vector algebra to develop the integrals. The various forms of the solution flow naturally from the integrals. In the second part, several modern perturbation techniques are developed and applied to cases of practical importance. For example, the perturbed two-body problem for an oblate planet or for a nonsymmetric rotating planet is considered, as is the effect of drag on a satellite. The two-body problem is regularized, and the nonlinear differential equation is thereby transformed to a linear one by further embedding several of the integrals. Finally, a brief sketch of numerical methods is given, as the perturbation equations must be solved by numerical rather than by analytical methods.
Author: William E. Wiesel
Publisher: CreateSpace
ISBN: 9781453781470
Category : Technology & Engineering
Languages : en
Pages : 218
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Book Description
Beginning with Hamiltonian dynamics, Modern Astrodynamics blends the modern methods of dynamical systems theory with the perturbation theory methods of the last century. With an emphasis on earth satellite motion, the derivation of the geopotential expansion is covered, and the motion of an object under the influence of the Earth's equatorial oblateness is derived to the first order. The structure of the phase space of Hamiltonian systems is explored both with modern numerical techniques (the surface of section) periodic orbit theory, and nonlinear resonance methods. The text concludes with applications of these modern methods to the problem of the relative motion of satellites in orbit about the earth, and the application of KAM tori to earth satellite motion. The text is suitable for a semester course at the introductory graduate level. Topics covered include: (1) Modern Numerical Methods, (2) Transformation Theory, (3) Variation of Elements, (4) Perturbing Forces, (5) General Perturbations, (6) Nonlinear Resonance, (7) Relative Satellite Motion, and (8) KAM Tori.
Author: Roger R. Bate
Publisher: Courier Corporation
ISBN: 9780486600611
Category : Technology & Engineering
Languages : en
Pages : 484
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Book Description
Teaching text developed by U.S. Air Force Academy and designed as a first course emphasizes the universal variable formulation. Develops the basic two-body and n-body equations of motion; orbit determination; classical orbital elements, coordinate transformations; differential correction; more. Includes specialized applications to lunar and interplanetary flight, example problems, exercises. 1971 edition.
Author: Marshall H. Kaplan
Publisher: Courier Dover Publications
ISBN: 0486819183
Category : Technology & Engineering
Languages : en
Pages : 433
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Book Description
Topics include orbital and attitude maneuvers, orbit establishment and orbit transfer, plane rotation, interplanetary transfer and hyperbolic passage, lunar transfer, reorientation with constant momentum, attitude determination, more. Answers to selected exercises. 1976 edition.
Author: P. Guptil
Publisher:
ISBN: 9780750681575
Category : Technology & Engineering
Languages : en
Pages : 0
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Book Description
Author: Alessandro de Iaco Veris
Publisher: Springer
ISBN: 331962220X
Category : Technology & Engineering
Languages : en
Pages : 1309
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Book Description
This modern textbook guides the reader through the theory and practice of the motion and attitude control of space vehicles. It first presents the fundamental principles of spaceflight mechanics and then addresses more complex concepts and applications of perturbation theory, orbit determination and refinement, space propulsion, orbital maneuvers, interplanetary trajectories, gyroscope dynamics, attitude control, and rocket performance. Many algorithms used in the modern practice of trajectory computation are also provided. The numerical treatment of the equations of motion, the related methods, and the tables needed to use them receive particular emphasis. A large collection of bibliographical references (including books, articles, and items from the "gray literature") is provided at the end of each chapter, and attention is drawn to many internet resources available to the reader. The book will be of particular value to undergraduate and graduate students in aerospace engineering.
Author: Howard D Curtis
Publisher: Elsevier
ISBN: 0080887848
Category : Technology & Engineering
Languages : en
Pages : 744
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Book Description
Orbital Mechanics for Engineering Students, Second Edition, provides an introduction to the basic concepts of space mechanics. These include vector kinematics in three dimensions; Newton’s laws of motion and gravitation; relative motion; the vector-based solution of the classical two-body problem; derivation of Kepler’s equations; orbits in three dimensions; preliminary orbit determination; and orbital maneuvers. The book also covers relative motion and the two-impulse rendezvous problem; interplanetary mission design using patched conics; rigid-body dynamics used to characterize the attitude of a space vehicle; satellite attitude dynamics; and the characteristics and design of multi-stage launch vehicles. Each chapter begins with an outline of key concepts and concludes with problems that are based on the material covered. This text is written for undergraduates who are studying orbital mechanics for the first time and have completed courses in physics, dynamics, and mathematics, including differential equations and applied linear algebra. Graduate students, researchers, and experienced practitioners will also find useful review materials in the book. NEW: Reorganized and improved discusions of coordinate systems, new discussion on perturbations and quarternions NEW: Increased coverage of attitude dynamics, including new Matlab algorithms and examples in chapter 10 New examples and homework problems
