Geometric Properties Completely Characterizing, the Set of All the Curves of
Language: English
Published by Forgotten Books, 2020
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
AbeBooks seller since June 2, 2021
Condition: New
US$ 17.43
Quantity: Over 20 available
Add to basketItem description from seller
Print on Demand. This book is a comparative analysis of curves along which constrained motion is possible, such that the pressure of the moving particle against the curve is either proportional to the normal component of the force or constant. The author, a University Professor, examines previous work on this subject and in so doing develops new geometric properties to supplement two previously identified properties of the subject. Expanding on the work of Sarah Elizabeth Cronin, the author proves that the first set of curves, dependent on a single parameter, has four properties. These properties show that the curves have osculating parabolas whose foci lie on a circle through the given point and hyperosculating circles whose centers lie on a conic through the given point. The author then proves that the second set of curves, dependent on two parameters, has eight properties. Several of these properties serve to geometrically construct the force vector in the field of force. Others show that the curves have osculating conics whose centers lie on a conic through the given point, a radius of curvature of conic I one-tenth the difference between the radius of curvature of conic I and the given curvature element, and a locus of the second center of curvature of conic I that is a cubic curve passing through the given point. The book shows the two sets of curves are characterizable solely by these properties, and through this work the author has added significantly to the body of knowledge on the subject of curves of constant pressure in a field of force. 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.…
Seller Inventory # 9781331823070_0
- Title
- Geometric Properties Completely Characterizing, the Set of All the Curves of
- Author
- Eugenie Maria Morenus
- Publisher
- Forgotten Books
- Publication year
- 2020
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1331823072
- ISBN 13
- 9781331823070
- Seller catalogs
- Geometry
Explore the geometry of motion in a force field and how curves can carry constant pressure.
This concise, authoritative work examines curves in a plane field of force where a moving particle experiences constant pressure against its path. It develops an intrinsic differential framework to describe how such curves are shaped, constrained, and connected to the underlying force field. The book presents a clear sequence of properties that uniquely characterize these curves and shows how varying the governing parameter yields a family of solutions.
Designed for readers with an interest in applied mathematics and geometric theory, it links vector forces, curvature, and the motion of constrained particles in an accessible, rigorous way. The discussion blends visual geometry with precise equations, offering a path from fundamental definitions to the complete characterization of the curve systems.
- Foundations: how pressure against a curve relates to normal acceleration and the force field.
- Intrinsic and Cartesian descriptions: translating between abstract relations and coordinate form.
- Osculating shapes: parabolas, conics, and how centers of curvature trace guiding curves.
- Parameters and families: how a single constant pressure parameter generates multiple curve sets and their properties.
Ideal for readers of advanced geometry and applied dynamics who want a rigorous, self-contained treatment of curves defined by constant pressure in a field of force.
"Synopsis" may belong to another edition of this title.
Forgotten Books
London, United Kingdom
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Forgotten Books’ Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the quality of the aged text.
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