Counting on Frameworks（I***N=9780883853313） mobi 下载 网盘 caj lrf pdf txt 阿里云

C***ider a scaffolding that is c***tructed by bolting together rods and beams. The ultimate question is whether the structure is strong enough to *** 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 c***ideration is modelled as a framework. These models are the degrees of *** model and two models based on quadratic equati*** and linear equati*** respectively. The author shows that all three of these models agree except for a very small class of specially c***tructed frameworks. This is a theory with significant practical applicati*** 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 Moti***

 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

Applicati***

 4.1  A Short History of Rigidity

……

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书籍介绍

C***ider a scaffolding that is c***tructed by bolting together rods and beams. The ultimate question is whether the structure is strong enough to *** 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 c***ideration is modelled as a framework. These models are the degrees of *** model and two models based on quadratic equati*** and linear equati*** respectively. The author shows that all three of these models agree except for a very small class of specially c***tructed frameworks. This is a theory with significant practical applicati*** and will be of interest to a wide range of people including those studying graph theory or mathematical modelling.