Essays on the Motion of Celestial Bodies

by Beletskii, V. V.; Iacob, A.

• ISBN13: 9783764358662
• ISBN10: 3764358661
• Format: Hardcover
• Copyright: 2002-01-01
• Publisher: Birkhauser

Summary

The development of the mechanics of space flight brought to life a whole series of fascinating and novel problems. The purpose of this book is to present some interesting and often unexpected achievements that have allowed some classical problems to be reconsidered in a new light. In order to reveal the beauty of the research process leading to the results, the emphasis is put on the analysis that can be carried out on the level of graphs and drawings, and sometimes numbers. Whenever possible, the investigation relies on maximally intuitive, elegant geometric tools. The book can be read profitably by anyone with the mathematical background typically offered in the first few years of undergraduate studies in mathematics, physics and engineering, including students, teachers, scientists and engineers. From the review of the first edition in Priroda by V.I. Arnold and Ya.B. Zeldovich: "...For a solid scientific monograph, V.V. Beletsky's book is out of the ordinary in many respects. Without exaggeration we can say that it marks the affirmation of a new style in the scientific literature. The author explains in a frank and detailed manner the reasons behind each calculation, its difficulties, and the psychological side of research. ...The general impression that the "Essays" make is not that of a boring lesson, but rather a discussion with a brilliant, knowledgeable and wise interlocutor."

Table of Contents

Dedication	xiii
A word from the author	xv
On the unperturbed and perturbed motion of a satellite, with a digression on asymptotic methods of nonlinear mechanics	1	(42)
Lucky us!	1	(4)
Keplerian motion	5	(4)
Perturbed motion. Osculating elements	9	(2)
Osculating orbit of an equatorial satellite	11	(5)
The equations in osculating elements. Delaunay elements	16	(5)
Digression on asymptotic methods of nonlinear mechanics. Oscillations of a satellite about its center of mass. Averaging of canonical equations	21	(15)
Satellite in the gravitational field of Earth	36	(7)
On the rebirth of an old problem, or what happens if two masses are placed at a purely imaginary distance from one another	43	(22)
From Euler to our days	43	(1)
The connection between the two problems	44	(6)
Integration. Coordinate system	50	(2)
The Hamilton-Jacobi method	52	(1)
Integration	53	(3)
The region of motion of a satellite	56	(3)
Jacobi's elliptic functions	59	(3)
The motion of a polar Earth satellite	62	(3)
Yet another reincarnation of an old problem	65	(24)
And what sort of problem is that?	65	(2)
Briefly on the equations of motion and their integration	67	(3)
Plane motion	70	(2)
Description of the trajectories of plane motion	72	(11)
A few words about the influence of radiation pressure on the motion of Earth satellites	83	(6)
Motion of the worlds	89	(32)
One more time about the ``Laplace Theorem'' and other [Serious] ``Things''	89	(6)
Wouldn't you like to see the Moon fall on Earth?	95	(7)
The region of weakly-perturbed motion	102	(3)
Stability of the Solar System	105	(6)
Is the Solar System resonant?	111	(10)
The restricted three-body problem, flight to the Moon, and galactic evolution	121	(18)
The Hill surfaces	121	(5)
Digression on libration points	126	(2)
Moon intercept trajectories and a method for their investigation	128	(4)
Galactic evolution	132	(7)
They are waltzing in orbits	139	(68)
Gravitational potential	139	(3)
Rotation of the Moon. Background material on stability theory	142	(5)
Stability of relative equilibrium in a gravitational field	147	(4)
Rhinogradentia in orbit	151	(1)
Passive stabilization of artificial satellites	152	(1)
Nonlinear oscillations	153	(6)
Fast rotations	159	(4)
Where the author slightly frightens the reader	163	(2)
Explicit form of the perturbed motion	165	(2)
Pegasus	167	(5)
Moon, Mercury, resonances	172	(5)
Schiaparelli and others	177	(2)
Resonant rotations of celestial bodies and the generalized Cassini laws	179	(13)
Tendency toward synchronization of rotational motion in complex gravitational fields. Lunar-solar precession and nutation of the Earth's axis	192	(2)
A model of tidal phenomena and capture into resonant rotation	194	(3)
Magnetic and magneto-gravitational stabilization	197	(10)
In a spiral to space	207	(20)
Low thrust	207	(1)
Escape parameters and paradoxes	207	(9)
A monotone escape spiral	216	(6)
Arbitrary trajectories with small eccentricities	222	(5)
The full force of the sun blows in the sails	227	(18)
The gravity flyer	245	(20)
Force of attraction on a body of non-negligible dimensions	245	(2)
A pulsating spaceship	247	(4)
Left behind by your spaceship? Swim breaststroke!	251	(4)
The gravity flyer and the reader	255	(2)
The gravity flyer as a resonance phenomenon	257	(3)
The gravity flyer and writers	260	(5)
Interplanetary flights: low trusts for high goals	265	(36)
Prelude	265	(1)
Larger payloads, less fuel	266	(1)
The Pontryagin maximum principle	267	(3)
The equation of optimal flight	270	(2)
No constraints	272	(1)
The method of carrier trajectories	273	(3)
The scheme for solving the boundary value problem	276	(1)
Integration	277	(6)
Some problems of relative motion	283	(2)
Computational results for optimal interplanetary trajectories	285	(7)
Presentation of results of the computation of series of trajectories	292	(5)
Correction of interplanetary trajectories	297	(4)
Relative motion of orbiting bodies	301	(36)
In orbit--two satellites	301	(4)
The equations of relative motion	305	(1)
Free motion of an astronaut relative to his spaceship	306	(3)
Leonov and the lens cap	309	(2)
Space probe	311	(2)
Boleadoras in space	313	(6)
The evolution of mixed motion	319	(5)
System of linked bodies in space	324	(3)
Cloud of particles in orbit and the Poincare recurrence theorem	327	(10)
Cosmic pinwheel	337	(16)
The Proton satellites	337	(22)
Here is how all this was discovered	359
What was discovered	342	(2)
Here is how all this is explained	344	(9)
References	353	(16)
Author index	369	(2)
Subject index	371