Title: Geometric Properties Completely, Characterizing All the Curves, in a Plane Along Which the Constrained Strained Motion Is Such That the Pressure Is Proportional to the Normal Component of the Acting Force (Classic Reprint)
Publisher: Forgotten Books
Publication Date: 2019
Language: English
ISBN 10: 0267800487
ISBN 13: 9780267800483
Binding: HRD
Condition: New
Weight: 275 grams

About this title

Synopsis

Explore the geometry of curves shaped by a constant pressure along a moving line of force.

This nonfiction work studies how a particle travels in a plane under a position-based force and a pressure relation P = kN. It presents a complete, exact description of the family of curves defined by this rule and shows how their shapes are tied to a single differential equation, written in both intrinsic and Cartesian forms. The book reveals how the motion depends on initial direction and speed, yielding a rich, quadruply infinite array of trajectories.

Two clear sections frame the value:

It derives the governing equations and then examines the geometric properties that characterize all curves in the family.
It connects special cases to familiar curves, like trajectories, brachistochrones, catenaries, and velocity curves, illustrating how they arise from particular parameter choices.

What you’ll experience

A detailed look at how centers of osculating conics trace out new curves at each point.
Visualizations of how curvature, tangents, and normal components interact under the pressure rule.
Step-by-step reasoning that links intrinsic forms to Cartesian forms, plus implications for multiple systems.

What you’ll learn

How to identify and describe infinite families of curves governed by a single law.
Ways to interpret geometric properties such as centers of curvature, osculating conics, and higher-order contacts.
The connections between general theory and the four “special cases of physical interest” that relate to common trajectory types.

Ideal for readers of advanced geometry and applied mathematics who want a rigorous, self-contained treatment of curve systems shaped by a proportional pressure constraint. If you enjoy exploring how abstract equations translate into tangible geometric behavior, this edition offers a thorough, methodical study.

"About this title" may belong to another edition of this title.

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