Stability of Ships and Other Bodies

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Abstract
	Why Abstract
	Short Abstract
Prologue For This Book
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Acknowledgment
CONTRIBUTORS LIST
	How to contribute to this book
	Credits
		Steven from artofproblemsolving.com
		Dan H. Olson
		Richard Hackbarth
		Kosamo Mazer
		John Motanizitz
		Jimi Tan
		Ahsan Ibn Muhammed Ibn Yusuf
		Various Rolling researchers
		Galina Yakovlevna Dynnikova
		Your name here
		Typo corrections and other \"minor\" contributions
Nomenclature
The Book Change Log
	Version 0.8.2
		April 13, 2022 (7.4M 283 pages)
		April 13, 2022 (7.4M 283 pages)
	Version 0.8.0
		March 17, 2022 (7.3M 277 pages)
		Mach 25, 2022 (7.3M 277 pages)
	Version 0.7.5
		Jan 17, 2022 (7.0M 261 pages)
		Oct 26, 2021 (7.0M 261 pages)
	Version 0.7.0
		Oct 26, 2021 (5.3M 229 pages)
	Version 0.6.5
		Sep 26, 2021 (4.5M 205 pages)
	Version 0.6.0
		Sep 26, 2021 (4.5M 205 pages)
	Version 0.5.5
		Aug 22, 2021 (3.9M 179 pages)
	Version 0.5.2
		July 1, 2021 (3.5M 167 pages)
	Version 0.5.1
		June 25, 2021 (3.5M 163 pages)
	Version 0.5.0
		June 15, 2021 (3.3M 159 pages)
Copyright Notice
	GNU Free Documentation License
	Preamble
	1. Applicability And Definitions
	2. Verbatim Copying
	3. Copying In Quantity
	4. Modifications
	5. Combining Documents
	6. Collections Of Documents
	7. Aggregation With Independent Works
	8. Translation
	9. Termination
	10. Future Revisions Of This License
	Addendum: How to use this License for your documents
How This Book Has Been Written
	How cooperation work
	The Smart–ass Questions
	More info
	Initial
Preface
Introduction to Stability
	What is Stability of Floating Bodies?
	History of Ship Stability
		Original History
		Recent Developments
	Rolling Rotation
	Summary
Marine Bodies Definitions
	Opening Remarks on Definitions
		Salinity and temperature effects
		Load Lines
		Tonne Per Centimeter
		Deviations From the Design
		Ship Length
		Ship Length
	Special Dimensions of the Ships
	Summary
Mathematics For Stability
	Differentiation
	Integration
	Vectors and Coordinates System
		Vector Algebra
		Cylindrical Coordinates
	Numerical Analysis
	Integration
	Simpson\'s Rule
	Summary
Mass Centroid
	Actual Mass Centroid
	Approximate Centroid of Area
	Change of Centroid Location Due to Area Change
	Change of Mass Centroid Due to Addition or Subtraction of Mass in 3D
		A Small Change in Angle of Rotation
	Transformation of Coordinates
	Appendix
Moment of Inertia
	Moment of Inertia for Mass
	Moment of Inertia for Area
		General Discussion
	The Parallel Axis Theorem
	Examples of Moment of Inertia
	Product of Inertia
		Transfer of Axis Theorem
	Principal Axes of Inertia
Pressure
	Introduction
	Fluid Forces on Surfaces
		Fluid Forces on Straight Surfaces
		Pressure Center
	Pressure on Floating Body
	Summary
Buoyancy
	Introduction
	Examples
	Applications of Buoyancy
	Practical questions
Direct Examination
	Introduction
	Centroid of Floating Body or Buoyancy Centroid
	Introduction to Direct Examination Method
	The Direct Examination
		Usage of Stability to find Centroid
	Potential Energy Approach
Metacenter
	Introduction
	Application of GM-.4
		Unstable Bodies, Negative GM-.4
	The G-.4Z-.4 diagram
	Stability of Body with Shifting Mass Centroid
		Neutral frequency of Floating Bodies
		Limitations
	Metacentric Height, GM-.4, Measurement
	Stability of Submerged Bodies
	Stability of None Systematical or ``Strange\'\' Bodies
Variable Density Floating Bodies
Added Mass and Transfer Properties
	Introduction
	History
	What is the Added Mass?
	The Added Mass Matrix of a Body
		Added Moment of Inertia Coefficients
	Calculations of the Added Mass
	Transfer Mechanisms and Transfer Properties
		History of Transfer Properties
		Introduction
		Transfer Linear Motion to Rotating Motion
		The Parallel Axes Theorem for Added Mass
		Experimental Observation
	Added Mass and Transfer Properties
	Added Moment of Inertia
	Appendices
	Introduction
Rolling
	Introduction
		The Quasi–State Foundation
	Historical Background
	Physical Considerations
		The Effect of Added Properties
		The change of density effect
	Rolling Governing Equations
	The Simplest Case
	Appendices
	Double Pendulum: Simplifications
		Double Pendulum with Point Masses
		Double Pendulum with Circular Motion with Mass Distribution
		Double Pendulum with Linear Motion
	Floating in Heave Movement
	Pendulum With Moving Hinge Point
	Change of Center of Rotation
Dimensional Analysis
	Introductory Remarks
		Brief History
		Theory Behind Dimensional Analysis
		Dimensional Parameters Application for Experimental Study
		The Pendulum Class Problem
	Buckingham—-Theorem
		Construction of the Dimensionless Parameters
		Similarity and Similitude
	Summary
Experiments for Stability
	Introduction
	Stability Points of Various Bodies
		Concept
		Description
		Apparatus
		Procedure
		Data Analysis
		Additional Questions
	Cylinder Stability Diagram
		Concept
		Description
		Apparatus
	The procedure
		Data Analysis
		Additional Questions
	GM-.4 experiments
		Concept
		Description
		Rig
		Procedure
		Measurements
		Data Analysis
		Additional Questions
		References
Data-.4
Bibliography
Index