Download Celestial Mechanics: The Waltz of the Planets (Springer by Alessandra Celletti (Author), Ettore Perozzi (Author) PDF

By Alessandra Celletti (Author), Ettore Perozzi (Author)

The purpose of this ebook is to illustrate to a much broader viewers, in addition to to a extra expert viewers, the numerous attention-grabbing elements of contemporary celestial mechanics. It units out to do that with no using arithmetic. After giving the reader the technical instruments wanted for a easy figuring out of the underlying actual phenomena (using in simple terms ordinary mathematics), evidence and figures are supplied on ancient occasions, smooth discoveries and destiny functions. Contents are divided into significant themes the place the 3 "souls" of contemporary celestial mechanics (dynamical platforms, sunlight approach and stellar platforms, spaceflight dynamics) play a massive position.

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Additional info for Celestial Mechanics: The Waltz of the Planets (Springer Praxis Books Popular Astronomy)

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KAM theory simply provides a lower estimate of the chaotic transition. The farther we go from a safe KAM estimate, the easier it is to become caught in chaotic motion. 8. N. I. Arnold and ). Moser. KAM and all t h a t 37 In this respect KAM theory can be compared to the trials for testing the roadholding power of a vehicle. The general stability of a car travelling on a winding road is granted only for relatively low velocities. Once a certain value is achieved, stability depends upon the skill of the driver; but it eventually becomes impossible to keep control of the car, even by a professional race driver.

In other words, we have found a periodic orbit with a period of twice the time spent between the occurrence of the two mirror configurations. MAPPING CHAOS The dynamical behaviour of an integrable system, such as the two-body problem, can be predicted with high accuracy once the mathematical solution of its equations of motion is determined. Conversely, chaotic behaviour is typical of non-integrable systems and becomes increasingly dominant as the complexity of the system grows. The three-body problem is not integrable, and thus we can expect that sooner or later chaos will arise.

A chaos machine and t h e butterfly effect In order to grasp the exact meaning of 'chaotic motion' it is possible to show how to build a simple machine exhibiting an extremely complex behaviour: a chaos machine. Take a bicycle wheel and fix it to the ground so that it can rotate freely, and on each spoke hang a small plastic container with a hole at the bottom. Then pour a steady flux of water over the wheel so that it fills the containers as they pass under it. The different weight of the containers, filled in turn by water and emptied through the holes, drives the rotation of the wheel.

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