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E-raamat: Dynamics: Theory and Application of Kane's Method

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  • Formaat: EPUB+DRM
  • Ilmumisaeg: 09-Mar-2016
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781316053508
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  • Formaat: EPUB+DRM
  • Ilmumisaeg: 09-Mar-2016
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781316053508
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This book is ideal for teaching students in engineering or physics the skills necessary to analyze motions of complex mechanical systems such as spacecraft, robotic manipulators, and articulated scientific instruments. Kane's method, which emerged recently, reduces the labor needed to derive equations of motion and leads to equations that are simpler and more readily solved by computer, in comparison to earlier, classical approaches. Moreover, the method is highly systematic and thus easy to teach. This book is a revision of Dynamics: Theory and Applications (1985), by T. R. Kane and D. A. Levinson, and presents the method for forming equations of motion by constructing generalized active forces and generalized inertia forces. Important additional topics include approaches for dealing with finite rotation, an updated treatment of constraint forces and constraint torques, an extension of Kane's method to deal with a broader class of nonholonomic constraint equations, and other recent advances.

Arvustused

'Dynamics: Theory and Application of Kane's Method is a timely update of the now classical book by Kane and Levinson by two authors, collectively with many decades of experience stretching across academia and government laboratories. While providing coverage of a broader class of problems and of recent advances in the field, the rigor and clarity of the original text is retained. This new book will be welcomed by many working on dynamics and control of complex mechanical and aerospace multibody systems.' Olivier A. Bauchau, Journal of Computational and Nonlinear Dynamics Full review available at https://doi.org/10.1115/1.4034731

Muu info

This book presents Kane's method, a modern approach that leads economically to equations that can be readily solved by computer.
Preface ix
Preface to Dynamics: Theory and Applications xi
To the Reader xv
1 Differentiation of Vectors
1(18)
1.1 Simple Rotation
2(1)
1.2 Direction Cosine Matrix
2(1)
1.3 Successive Rotations
3(3)
1.4 Vector Functions
6(1)
1.5 Several Reference Frames
7(1)
1.6 Scalar Functions
7(2)
1.7 First Derivatives
9(2)
1.8 Representations of Derivatives
11(1)
1.9 Notation for Derivatives
12(1)
1.10 Differentiation of Sums and Products
13(1)
1.11 Second Derivatives
14(1)
1.12 Total and Partial Derivatives
15(2)
1.13 Scalar Functions of Vectors
17(2)
2 Kinematics
19(20)
2.1 Angular Velocity
19(5)
2.2 Simple Angular Velocity
24(3)
2.3 Differentiation in Two Reference Frames
27(1)
2.4 Auxiliary Reference Frames
28(2)
2.5 Angular Acceleration
30(2)
2.6 Velocity and Acceleration
32(2)
2.7 Two Points Fixed on a Rigid Body
34(1)
2.8 One Point Moving on a Rigid Body
35(4)
3 Constraints
39(28)
3.1 Configuration Constraints
39(3)
3.2 Generalized Coordinates
42(2)
3.3 Number of Generalized Coordinates
44(1)
3.4 Motion Variables
45(3)
3.5 Motion Constraints
48(3)
3.6 Partial Angular Velocities, Partial Velocities
51(4)
3.7 Motion Constraints with Nonlinear Equations
55(2)
3.8 Partial Angular Accelerations, Partial Accelerations
57(3)
3.9 Acceleration and Partial Velocities
60(7)
4 Mass Distribution
67(33)
4.1 Mass Center
67(2)
4.2 Curves, Surfaces, and Solids
69(2)
4.3 Inertia Vector, Inertia Scalars
71(3)
4.4 Mutually Perpendicular Unit Vectors
74(2)
4.5 Inertia Matrix, Inertia Dyadic
76(5)
4.6 Parallel Axes Theorems
81(2)
4.7 Evaluation of Inertia Scalars
83(4)
4.8 Principal Moments of Inertia
87(10)
4.9 Maximum and Minimum Moments of Inertia
97(3)
5 Generalized Forces
100(34)
5.1 Moment about a Point, Bound Vectors, Resultant
100(4)
5.2 Couples, Torque
104(1)
5.3 Equivalence, Replacement
105(4)
5.4 Generalized Active Forces
109(4)
5.5 Forces Acting on a Rigid Body
113(3)
5.6 Contributing Interaction Forces
116(2)
5.7 Terrestrial Gravitational Forces
118(4)
5.8 Coulomb Friction Forces
122(6)
5.9 Generalized Inertia Forces
128(6)
6 Constraint Forces, Constraint Torques
134(29)
6.1 Constraint Equations, Acceleration, Force
134(2)
6.2 Holonomic Constraint Equations
136(2)
6.3 Linear Nonholonomic Constraint Equations
138(2)
6.4 Nonlinear Nonholonomic Constraint Equations
140(2)
6.5 Constraint Forces Acting on a Rigid Body
142(6)
6.6 Noncontributing Forces
148(10)
6.7 Bringing Noncontributing Forces into Evidence
158(5)
7 Energy Functions
163(28)
7.1 Potential Energy
163(10)
7.2 Potential Energy Contributions
173(5)
7.3 Dissipation Functions
178(1)
7.4 Kinetic Energy
179(3)
7.5 Homogeneous Kinetic Energy Functions
182(2)
7.6 Kinetic Energy and Generalized Inertia Forces
184(7)
8 Formulation of Equations of Motion
191(49)
8.1 Dynamical Equations
191(8)
8.2 Secondary Newtonian Reference Frames
199(3)
8.3 Additional Dynamical Equations
202(3)
8.4 Linearization of Dynamical Equations
205(8)
8.5 Systems at Rest in a Newtonian Reference Frame
213(4)
8.6 Steady Motion
217(3)
8.7 Motions Resembling States of Rest
220(3)
8.8 Generalized Impulse, Generalized Momentum
223(6)
8.9 Collisions
229(11)
9 Extraction of Information from Equations of Motion
240(66)
9.1 Integrals of Equations of Motion
240(3)
9.2 The Energy Integral
243(3)
9.3 The Checking Function
246(8)
9.4 Momentum Integrals
254(7)
9.5 Exact Closed-Form Solutions
261(4)
9.6 Numerical Integration of Differential Equations of Motion
265(12)
9.7 Determination of Constraint Forces and Constraint Torques
277(5)
9.8 Real Solutions of a Set of Nonlinear, Algebraic Equations
282(7)
9.9 Motions Governed by Linear Differential Equations
289(17)
10 Kinematics of Orientation
306(47)
10.1 Euler Rotation
306(3)
10.2 Direction Cosines
309(8)
10.3 Orientation Angles
317(9)
10.4 Euler Parameters
326(5)
10.5 Wiener-Milenkovic Parameters
331(3)
10.6 Angular Velocity and Direction Cosines
334(2)
10.7 Angular Velocity and Orientation Angles
336(5)
10.8 Angular Velocity and Euler Parameters
341(4)
10.9 Angular Velocity and Wiener-Milenkovic Parameters
345(8)
Problem Sets
353(130)
Problem Set 1 (Sees. 1.1--1.13)
353(4)
Problem Set 2 (Sees. 2.1--2.5)
357(6)
Problem Set 3 (Sees. 2.6--2.8)
363(8)
Problem Set 4 (Sees. 3.1--3.9)
371(9)
Problem Set 5 (Sees. 4.1--4.5)
380(5)
Problem Set 6 (Sees. 4.6--4.9)
385(4)
Problem Set 7 (Sees. 5.1--5.3)
389(3)
Problem Set 8 (Sees. 5.4--5.9)
392(11)
Problem Set 9 (Sees. 6.1--6.7)
403(7)
Problem Set 10 (Sees. 7.1--7.3)
410(6)
Problem Set 11 (Sees. 7.4--7.6)
416(4)
Problem Set 12 (Sees. 8.1--8.3)
420(10)
Problem Set 13 (Sees. 8.4--8.9)
430(10)
Problem Set 14 (Sees. 9.1--9.6)
440(9)
Problem Set 15 (Sees. 9.7--9.9)
449(19)
Problem Set 16 (Sees. 10.1--10.5)
468(7)
Problem Set 17 (Sees. 10.6--10.9)
475(8)
Appendix I Direction Cosines as Functions of Orientation Angles 483(5)
Appendix II Kinematical Differential Equations in Terms of Orientation Angles 488(5)
Appendix III Inertia Properties of Uniform Bodies 493(12)
Index 505
Carlos M. Roithmayr is a senior aerospace engineer in the Systems Analysis and Concepts Directorate at the NASA Langley Research Center in Hampton, Virginia. He earned a Bachelor of Aerospace Engineering degree at the Georgia Institute of Technology, both an M.S. and a Degree of Engineer in Aeronautics and Astronautics from Stanford University, and a Ph.D. in Aerospace Engineering from the Georgia Institute of Technology. He began his career with NASA at the Johnson Space Center in Houston, Texas. His research interests include dynamics of multibody mechanical systems, spacecraft attitude dynamics and control, and orbital mechanics, and he has contributed to a wide variety of Agency projects and missions. He is author or coauthor of numerous refereed journal papers. Dr Roithmayr is a senior member of the American Institute of Aeronautics and Astronautics. Dewey H. Hodges is a professor of aerospace engineering at the Georgia Institute of Technology. He holds a B.S. in Aerospace Engineering from the University of Tennessee at Knoxville and both M.S. and Ph.D. degrees in Aeronautics and Astronautics from Stanford University. His research interests include aeroelasticity, structural mechanics, rotorcraft dynamics, finite element analysis, and computational optimal control. He has authored or coauthored five books and more than 200 technical papers in refereed journals. Professor Hodges is a Fellow of the American Helicopter Society, the American Institute of Aeronautics and Astronautics, the American Society of Mechanical Engineers, and the American Academy of Mechanics. He serves on the editorial boards of the Journal of Fluids and Structures, the Journal of Mechanics of Materials and Structures, and Nonlinear Dynamics.