Counting on Frameworks（ISBN=9780883853313） 2025 chm pdf kindle rb azw3 下载 115盘

Consider a scaffolding that is constructed by bolting together rods and beams. The ultimate question is whether the structure is strong enough to support the workers and their equipment. This is the problem that motivates the area of mathematics known as rigidity theory. The purpose of this book is to develop a mathematical model for the rigidity of structures. In fact the author develops three distinct models in which the structure under consideration is modelled as a framework. These models are the degrees of freedom model and two models based on quadratic equations and linear equations respectively. The author shows that all three of these models agree except for a very small class of specially constructed frameworks. This is a theory with significant practical applications and will be of interest to a wide range of people including those studying graph theory or mathematical modelling.

Preface

1  Counting on Frameworks

 1.1  Designing Structures

 1.2  The Grid Bracing Problem

 1.3  Frameworks and Their Motions

 1.4  Degrees of Freedom

 1.5  More About the Grid Problem

 1.6  What Next?

2  Graph Theory

 2.1  1-Dimensional Rigidity (Part I)

 2.2  Graphs and Frameworks

 2.3  Fundamentals of Graph Theory

 2.4  Trees

 2.5  1-Dimensional Rigidity (Part II)

 2.6  The Solution to the Grid Problem

 2.7  Planar Graphs

3  Rigidity Theory

 3.1  Rigidity Comes in Two Flavors

 3.2  Infinitesimal Rigidity

 3.3  The Combinatorial Aspects of Rigidity

 3.4  Rigidity for Graphs

 3.5  Generic Rigidity in Dimension Two

 3.6  Generic Rigidity in 3-SpaceHistory and

Applications

 4.1  A Short History of Rigidity

……

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书籍介绍

Consider a scaffolding that is constructed by bolting together rods and beams. The ultimate question is whether the structure is strong enough to support the workers and their equipment. This is the problem that motivates the area of mathematics known as rigidity theory. The purpose of this book is to develop a mathematical model for the rigidity of structures. In fact the author develops three distinct models in which the structure under consideration is modelled as a framework. These models are the degrees of freedom model and two models based on quadratic equations and linear equations respectively. The author shows that all three of these models agree except for a very small class of specially constructed frameworks. This is a theory with significant practical applications and will be of interest to a wide range of people including those studying graph theory or mathematical modelling.