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E-raamat: Geometry for Naval Architects

(Associate Adjunct Professor, Faculty of Mechanical Engineering, Technion Israel Institute of Technology)
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  • Ilmumisaeg: 19-Nov-2018
  • Kirjastus: Butterworth-Heinemann Ltd
  • Keel: eng
  • ISBN-13: 9780081003398
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Geometry for Naval ArchitectsSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 19-Nov-2018
  • Kirjastus: Butterworth-Heinemann Ltd
  • Keel: eng
  • ISBN-13: 9780081003398
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Geometry for Naval Architects is the essential guide to the principles of naval geometry. Formerly fragmented throughout various sources, the topic is now presented in this comprehensive book that explains the history and specific applications of modern naval architecture mathematics and techniques, including numerous examples, applications, and references to further enhance understanding.

With a natural four-section organization (Traditional Methods, Differential Geometry, Computer Methods, and Applications in Naval Architecture), users will progress from basic fundamentals to specific applications. Careful instruction and a wealth of practical applications spare readers the extensive searches once necessary to understand the mathematical background of naval architecture and help them understand the meanings and uses of discipline-specific computer programs.

  • Explains the basics of geometry as applied to naval architecture, with specific practical applications included throughout the book for real-life insights
  • Presents traditional methods and computational techniques (including MATLAB)
  • Provides a wealth of examples in MATLAB and MultiSurf (a computer-aided design package for naval architects and engineers)
  • Includes supplemental MATLAB and MultiSurf code available on a companion site

Muu info

This comprehensive review of the basics of naval geometry explains the history and specific applications of modern naval architecture mathematics
About the Author xv
Preface xvii
The Organization of the Book
xix
Software
xx
Notation
xxi
Acknowledgements xxiii
Part 1 Traditional Methods
1 Elements of Descriptive Geometry
3(78)
1.1 Introduction
4(2)
1.2 Notations
6(1)
1.3 How We See - The Central Projection
6(2)
1.4 Central Projection
8(9)
1.4.1 Definition
8(1)
1.4.2 Properties
9(5)
1.4.3 Vanishing Points
14(3)
1.4.4 Conclusions on Central Projection
17(1)
1.5 A Note on Stereoscopic Vision
17(2)
1.6 The Parallel Projection
19(2)
1.6.1 Definition
19(1)
1.6.2 A Few Properties
19(1)
1.6.3 The Concept of Scale
20(1)
1.7 The Orthogonal Projection
21(4)
1.7.1 Definition
21(2)
1.7.2 The Projection of a Right Angle
23(2)
1.8 The Method of Monge
25(2)
1.9 Points
27(2)
1.10 Straight Lines
29(3)
1.10.1 The Projections of a Straight Line
29(2)
1.10.2 Intersecting Lines
31(1)
1.11 Planes
32(3)
1.12 An Example of Plane-Faceted Solid - The Cube
35(2)
1.13 A Space Curve - The Helix
37(1)
1.14 The Cylinder
38(3)
1.15 The Cone
41(3)
1.15.1 Introduction
41(1)
1.15.2 Points on the Cone Surface
42(2)
1.16 Conic Sections
44(8)
1.16.1 Introduction
44(1)
1.16.2 The Circle
45(1)
1.16.3 The Ellipse
46(2)
1.16.4 The Parabola
48(2)
1.16.5 The Hyperbola
50(2)
1.17 What Is Axonometry
52(9)
1.17.1 The Law of Scales
54(2)
1.17.2 Isometry
56(4)
1.17.3 An Ambiguity of the Isometric Projection
60(1)
1.18 Developed Surfaces
61(3)
1.18.1 What Is a Developed Surface
61(1)
1.18.2 The Development of a Cylindrical Surface
62(1)
1.18.3 The Development of a Conic Surface
63(1)
1.19 Summary
64(2)
1.20 Exercises
66(4)
Appendix 1.A The Connection to Linear Algebra and MATLAB
70(5)
Appendix 1.8 First Steps in MultiSurf
75(6)
2 The Hull Surface - Graphic Definition
81(40)
2.1 Introduction
81(5)
2.2 The Lines Drawing
86(3)
2.2.1 A Simple, Idealized Hull Surface
86(3)
2.3 Main Dimensions and Coefficients of Form
89(5)
2.4 Systems of Coordinates
94(1)
2.5 The Hull Surface of a Real Ship
95(1)
2.6 Consistency and Fairness of Ship Lines
96(6)
2.7 Drawing Instruments
102(1)
2.8 Table of Offsets
103(1)
2.9 Shell Expansion and Wetted Surface
104(4)
2.10 An Example in MultiSurf
108(8)
2.11 Summary
116(2)
2.12 Exercises
118(3)
3 Geometric Properties of Areas and Volumes
121(76)
3.1 Introduction
122(1)
3.2 Change of Coordinate Axes
123(2)
3.2.1 Translation of Coordinate Axes
123(1)
3.2.2 Rotation of Coordinate Axes
124(1)
3.3 Areas
125(6)
3.3.1 Definitions
125(2)
3.3.2 Examples
127(3)
3.3.3 Examples in Naval Architecture
130(1)
3.4 First Moments and Centroids of Areas
131(3)
3.4.1 Definitions
131(1)
3.4.2 Examples
132(1)
3.4.3 Examples in Naval Architecture
133(1)
3.5 Second Moments of Areas
134(22)
3.5.1 Definitions
134(2)
3.5.2 Parallel Translation of Axes
136(1)
3.5.3 Rotation of Axes
137(3)
3.5.4 The Tensor of Inertia
140(1)
3.5.5 Radius of Gyration
141(1)
3.5.6 The Ellipse of Inertia
142(1)
3.5.7 A Problem of Eigenvalues
143(3)
3.5.8 Examples
146(9)
3.5.9 Examples in Naval Architecture
155(1)
3.6 Volume Properties
156(5)
3.6.1 Definitions
156(1)
3.6.2 Examples
156(3)
3.6.3 Moments and Centroids of Volumes
159(2)
3.7 Mass Properties
161(2)
3.8 Green's Theorem
163(6)
3.9 Hull Transformations
169(8)
3.9.1 Numerical Calculations
170(2)
3.9.2 The 'One Minus Prismatic' Method
172(2)
3.9.3 Swinging the Curve
174(2)
3.9.4 Lackenby's General Method
176(1)
3.10 Applications
177(6)
3.10.1 The planimeter
177(5)
3.10.2 A MATLAB Digitizer
182(1)
3.11 Summary
183(5)
3.12 Exercises
188(9)
Part 2 Differential Geometry
4 Parametric Curves
197(26)
4.1 Introduction
197(1)
4.2 Parametric Representation
198(3)
4.3 Parametric Equation of Straight Line
201(3)
4.4 Curves in 3D Space
204(3)
4.4.1 The Straight Line
204(1)
4.4.2 Working With Parametric Equations
205(2)
4.4.3 The Helix
207(1)
4.5 Derivatives of Parametric Functions
207(2)
4.6 Notation of Derivatives
209(1)
4.7 Tangents
210(1)
4.8 Arc Length
210(1)
4.9 Arc-Length Parametrization
211(2)
4.10 The Curve of Centres of Buoyancy
213(6)
4.10.1 Parametric Equations
213(3)
4.10.2 A Theorem on the Axis of Inclination
216(1)
4.10.3 The Tangent and the Normal to the B-Curve
217(1)
4.10.4 Parametric Equations for Small Angles of Inclination
217(2)
4.11 Summary
219(1)
4.12 Exercises
220(3)
5 Curvature
223(36)
5.1 Introduction
223(1)
5.2 The Definition of Curvature
224(3)
5.2.1 Curvature in Explicit Representation
225(1)
5.2.2 Curvature in Parametric Representation
226(1)
5.3 Osculating Circle
227(6)
5.3.1 Definition
227(1)
5.3.2 Definition 1 detailed
227(1)
5.3.3 Definition 2 Detailed
228(2)
5.3.4 Definition 3 Detailed
230(1)
5.3.5 Centre of Curvature in Parametric Representation
231(2)
5.4 An Application in Kinematics - The Centrifugal Acceleration
233(3)
5.4.1 Position
233(1)
5.4.2 Velocity
234(1)
5.4.3 Acceleration
235(1)
5.5 Another Application in Mechanics - The Elastic Line
236(2)
5.6 An Application in Naval Architecture - The Metacentric Radius
238(1)
5.7 Differential Metacentric Radius
239(1)
5.8 Curves in Space
239(2)
5.9 Evolutes
241(1)
5.10 A Lemma on the Normal to a Curve in Implicit Form
242(2)
5.11 Envelopes
244(2)
5.12 The Metacentric Evolute
246(3)
5.13 Curvature and Fair Lines
249(1)
5.14 Examples
249(3)
5.15 Summary
252(2)
5.16 Exercises
254(1)
Appendix 5.A Curvature in MultiSurf
255(4)
6 Surfaces
259(46)
6.1 Introduction
259(1)
6.2 Parametric Representation
260(6)
6.3 Curves on Surfaces
266(1)
6.4 First Fundamental Form
267(3)
6.5 Second Fundamental Form
270(5)
6.6 Principal, Gaussian, and Mean Curvatures
275(3)
6.7 Ruled Surfaces
278(5)
6.7.1 Cylindrical Surfaces
279(1)
6.7.2 Conic Surfaces
280(1)
6.7.3 Surfaces of Tangents
281(1)
6.7.4 A Doubly-Ruled Surface, the Hyperboloid of One Sheet
282(1)
6.8 Geodesic Curvature
283(2)
6.9 Developable Surfaces
285(3)
6.10 Geodesics and Plate Development
288(2)
6.11 On the Nature of Surface Curvature
290(3)
6.12 Summary
293(3)
6.13 Exercises
296(2)
Appendix 6.A A Few MultiSurf Tools for Working With Surfaces
298(7)
Part 3 Computer Methods
7 Cubic Splines
305(20)
7.1 Introduction
305(2)
7.2 Cubic Splines
307(1)
7.3 The MATLAB Spline
308(2)
7.4 Working With Parametric Splines
310(2)
7.5 Space Curves
312(2)
7.6 Chord-Length Parametrization
314(2)
7.7 Centripetal Parametrization
316(1)
7.8 Summary
317(1)
7.9 Exercises
318(3)
Appendix 7.A MultiSurf - Cubic Spline, Polycurve
321(4)
8 Geometrical Transformations
325(36)
8.1 Introduction
325(3)
8.2 Transformations in the Plane
328(12)
8.2.1 Translation
328(1)
8.2.2 Rotation Around the Origin
329(1)
8.2.3 Rotation About an Arbitrary Point
330(2)
8.2.4 Reflection
332(1)
8.2.5 Isometries
332(2)
8.2.6 Shearing
334(1)
8.2.7 Scaling About the Origin
334(1)
8.2.8 Affine Transformations
335(2)
8.2.9 Homogeneous Coordinates
337(3)
8.3 Transformations in 3D Space
340(2)
8.4 Perspective Projections
342(6)
8.4.1 The Projection Matrix
342(3)
8.4.2 Ideal and Vanishing Points
345(2)
8.4.3 The Vanishing Line
347(1)
8.4.4 The Orthographic Projection as Limit of Perspective Projection
347(1)
8.5 Affine Combinations of Points
348(5)
8.5.1 Affine Combination of Two Points - Collinearity
348(2)
8.5.2 Alternative Proof of Collinearity
350(1)
8.5.3 Affine Combination of Three Points - Coplanarity
351(2)
8.6 Barycentres
353(1)
8.7 Summary
354(2)
8.8 Exercises
356(5)
9 Bezier Curves
361(26)
9.1 Introduction
361(2)
9.2 The First-Degree Bezier Curves
363(1)
9.3 The Second-Degree Bezier Curves
363(1)
9.4 The Third-Degree Bezier Curves
364(1)
9.5 The General Definition of Bezier Curves
365(2)
9.6 Interactive Manipulation of Bezier Curves
367(1)
9.7 De Casteljau's Algorithm
368(3)
9.8 Some Properties of Bezier Curves
371(4)
9.8.1 The First and the Last Point of the Curve
371(1)
9.8.2 End Tangents
372(1)
9.8.3 Convex Hull
372(1)
9.8.4 Variance Diminishing Property
373(1)
9.8.5 Invariance Under Affine Transformations
373(2)
9.9 Joining Two Bezier Curves
375(1)
9.10 Moving a Control Point
376(1)
9.11 Rational Bezier Curves
376(4)
9.12 Summary
380(1)
9.13 Exercises
381(6)
10 B-Splines and NURBS
387(24)
10.1 Introduction
387(1)
10.2 B-Splines
388(1)
10.3 Quadratic B-Splines
389(3)
10.4 Moving a Control Point
392(1)
10.5 A Cubic B-Spline
392(2)
10.6 Phantom Points
394(1)
10.7 Some Properties of the B-Splines
395(2)
10.8 NURBS
397(6)
10.9 Summary
403(2)
10.10 Exercises
405(3)
Appendix 10.A A Note on B-Splines and NURBS in MultiSurf
408(3)
11 Computer Representation of Surfaces
411(30)
11.1 Introduction
411(1)
11.2 Bezier Patches
412(8)
11.2.1 A Bilinear Patch
413(6)
11.2.2 Curve on Surface
419(1)
11.3 Bicubic Bezier Patch
420(5)
11.4 Joining Two Bezier Patches
425(3)
11.5 Swept Surfaces
428(2)
11.6 Lofted Surfaces
430(3)
11.7 Computer-Aided Design of Hull Surfaces
433(2)
11.8 Summary
435(1)
11.9 Exercises
436(2)
Appendix 11.A A Note on Surfaces in MultiSurf
438(3)
Part 4 Applications in Naval Architecture
12 Hull Transformations by Computer Software
441(12)
12.1 Introduction
441(1)
12.2 Affine Hulls
442(4)
12.3 A Note on Lackenby's Transformation
446(1)
12.4 Affine Combinations of Offsets
446(1)
12.5 Morphing
447(3)
12.6 Non-Linear Transformations
450(1)
12.7 Summary
450(1)
12.8 Exercises
451(2)
13 Conformal Mapping
453(18)
13.1 Introduction
453(1)
13.2 Working With Complex Variables
454(3)
13.3 Conformal Mapping
457(2)
13.4 Lewis Forms
459(9)
13.5 Summary
468(1)
13.6 Exercises
469(2)
Bibliography 471(8)
Answers to Selected Exercises 479(16)
Index 495
Adrian B. Biran received his MSc and DSc from Technion - Israel Institute of Technology, as well as a Diplomat Engineer degree from the Bucharest Polytechnic Institute. He worked extensively in design in Romania (at IPRONAV-The Institute of Ship Projects, the Bucharest Studios and IPA-The Institute of Automation Projects) and in Israel (at the Israel Shipyards and the Technion Research and Development Foundation). Dr. Biran has also worked as a project instructor in Romania at the Technical Military Academy and in Israel at the Ben Gurion University. He has taught subjects including Machine Design, Engineering Drawing, and Naval Architecture. He has authored several papers on subjects such as computational linguistics and computer simulations of marine systems and subjects belonging to Ship Design. He is also the author of Ship Hydrostatics and Stability, Second Edition (BH).
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