The Theory of Elliptic Integrals (Classic Reprint)

James Booth

ISBN 10: 1330872932 / ISBN 13: 9781330872932

Verlag: Forgotten Books, 2018

Beschreibung

Print on Demand. This book explores the motion of a rigid body around a fixed point when not acted upon by accelerating forces, drawing on the properties of ellipsoids, curves, and elliptic integrals. Motions of this kind are typically determined by differential equations, which the author presents in a manner accessible to those moderately versed in integral calculus. The author's incorporation of geometrical conceptions enhances clarity and simplicity, preserving the elegance of analysis. The book's main contribution is its reduction of the problem of motion of a rigid body to three positions: the positions of the axes, the axes themselves, and the body's motion during the defined time. This reduction is accomplished through the author's focus on the motion of a certain ellipsoid, where the axes of the ellipsoid are assumed proportional to the inverse square roots of the moments of inertia around the principal axes of the body, coinciding with them in direction. The author demonstrates that the time and other quantities must be determined by the aid of elliptic functions, then develops those functions, revealing previously unknown properties of these curves. The author also posits a new geometrical representative for elliptic functions of the first order, introducing a new curve with close analogies to the plane parabola, which they name the "spherical parabola." This curve is the gnomonic projection of a plane parabola touching a sphere at its focus. This discovery leads the author to establish the formula for the comparison of elliptic integrals of the third order, a formula usually attributed to Legendre. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.

Bestandsnummer des Verkäufers 9781330872932_0

Bibliografische Details

• Titel: The Theory of Elliptic Integrals (Classic Reprint)
• Verlag: Forgotten Books
• Erscheinungsjahr: 2018
• Sprache: Englisch
• ISBN-10: 1330872932
• ISBN-13: 9781330872932
• Einband: Paperback
• Zustand: New
• Buchtyp: print-on-demand item
• Verkäuferkataloge:
  • Calculus

Über diesen Titel

Inhaltsangabe

Excerpt from The Theory of Elliptic Integrals: And the Properties of Surfaces of the Second Order

The idea of substituting, as a means of investigation, an ideal ellipsoid, having certain relations with the actually revolv ing body, claims the illustrious Legendre as its author. Al though he conducts his own investigations on principles altogether different, be yet seems well aware of the use which might be made of this happy conception. In his Traz'té dc.

About the Publisher

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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.