Modern astrodynamics : fundamentals and perturbation methods
著者
書誌事項
Modern astrodynamics : fundamentals and perturbation methods
Princeton University Press, c1996
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注記
Includes bibliographical references (p. [243]-246) and index
内容説明・目次
内容説明
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.
目次
Preface1Background32The Two-Body Problem123Kepler's Laws314Methods of Computation405The f and g Functions586Two-Point Boundary Value Problems817Applications918Perturbation Theory1179Special Perturbation Methods14710Runge-Kutta Methods18411Types of Perturbations198Appendixes215A. Coordinate Transformations217B. Hyperbolic Motion225C. Conic Sections230D. Transfer-Angle Resolution233E. Stumpff Functions236F. Orbit Geometry239References243Index247
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