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Mechanics and Dynamical Systems with Mathematica® 2000 ed. [Kõva köide]

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Mechanics and Dynamical Systems with Mathematica® 2000 ed.Suurem pilt
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Püsilink: https://www.kriso.ee/db/9780817640071.html
Märksõnad:
Modeling and Applied Mathematics Modeling the behavior of real physical systems by suitable evolution equa­ tions is a relevant, maybe the fundamental, aspect of the interactions be­ tween mathematics and applied sciences. Modeling is, however, only the first step toward the mathematical description and simulation of systems belonging to real world. Indeed, once the evolution equation is proposed, one has to deal with mathematical problems and develop suitable simula­ tions to provide the description of the real system according to the model. Within this framework, one has an evolution equation and the re­ lated mathematical problems obtained by adding all necessary conditions for their solution. Then, a qualitative analysis should be developed: this means proof of existence of solutions and analysis of their qualitative be­ havior. Asymptotic analysis may include a detailed description of stability properties. Quantitative analysis, based upon the application ofsuitable methods and algorithms for the solution of problems, ends up with the simulation that is the representation of the dependent variable versus the independent one. The information obtained by the model has to be compared with those deriving from the experimental observation of the real system. This comparison may finally lead to the validation of the model followed by its application and, maybe, further generalization.

Arvustused

"The Mathematica notebook files are well written. Most procedures are quite general and may be adapted to different models. The book covers a huge amount of ground The nice thing about this book is the great variety of mathematical models treated."   Mathematical Reviews









"Solid motivations are always given. The book includes a great number of examples, taken from practice, many of them being worked out completely. [ It is] useful for practitioners and even mathematicians could find a lot of very interesting examples and motivations."   Mathematica, Revue dAnalyse Numerique et de Theorie de lApproximation









"A distinguishing feature of this books treatment of classical mechanics is the way in which it presents modeling, analysis and computation in a unified manner. This text gives a surprisingly readable yet thorough account of classical mechanics and the use of Mathematica to aid the numerical and analytic solution of many standard problems. It is aimed at advanced undergraduate students and is, in fact, [ a] very student-friendly text. There are many step-by-step descriptions of problem-solving methods that may be applied to broad classes of problems. This book will be of great use to those struggling with advanced applications and concepts."   Scientific Computing World



"In this advanced undergraduate book on analytical mechanics, [ the authors] develop enough of the theory of dynamical systems to provide an appropriate mathematical context for mechanics as well as useful analytical tools. They also provide Mathematica computer routines (available at the publisher's Web site) so the reader can visualize and experiment with the book's examples. This powerful combination of qualitative and quantitative tools allows for the analysis of a rich range of topics and material including some outside of mechanics.Still, the volume is fundamentally a textbook on classical mechanics and can be recommended as such, perhaps more than as a fundamental addition to a library collection."   Choice

Muu info

Springer Book Archives
Preface ix
I Mathematical Methods for Differential Equations
Models and Differential Equations
1(18)
Introduction
1(1)
Mathematical Models and Computation
2(6)
Examples of Mathematical Models
8(8)
Validation, Determinism, and Stochasticity
16(3)
Models and Mathematical Problems
19(38)
Introduction
19(1)
Classification of Models
20(6)
Statement of Problems
26(3)
Solution of Initial-Value Problems
29(11)
Representation of the Dynamic Response
40(6)
On the Solution of Boundary-Value Problems
46(4)
Problems
50(7)
Stability and Perturbation Methods
57(36)
Introduction
57(6)
Stability Definitions
63(2)
Linear Stability Methods
65(6)
Nonlinear Stability
71(5)
Regular Perturbation Methods
76(11)
Problems
87(6)
II Mathematical Methods of Classical Mechanics
Newtonian Dynamics
93(46)
Introduction
93(2)
Principles of Newtonian Mechanics
95(7)
Balance Laws for Systems of Point Masses
102(4)
Active and Reactive Forces
106(16)
Constraints and reactive forces
107(8)
Active forces and force fields
115(7)
Applications
122(14)
Dynamics of simple pendulum
123(2)
Particle subject to a central force
125(4)
Heavy particle falling in air
129(4)
Three-point masses subject to elastic forces
133(3)
Problems
136(3)
Rigid Body Dynamics
139(44)
Introduction
139(1)
Rigid Body Models
140(8)
Active and Reactive Forces in Rigid Body Dynamics
148(4)
Constrained Rigid Body Models
152(10)
Articulated Systems
162(3)
Applications
165(13)
Rigid body model of a vehicle and plane dynamics
166(1)
Compound pendulum
167(3)
Uniform rotations
170(1)
Free rotations of a gyroscope
171(3)
Ball on an inclined plane
174(4)
Problems
178(5)
Energy Methods and Lagrangian Mechanics
183(50)
Introduction
183(2)
Elementary and Virtual Work
185(4)
Energy Theorems
189(5)
The Method of Lagrange Equations
194(6)
Potential and First Integrals
200(7)
Energy Methods and Stability
207(4)
Applications
211(16)
Three body articulated system
212(2)
Stability of Duffing's model
214(3)
Free rotations or Poinsot's motion
217(3)
Heavy gyroscope
220(4)
The rolling coin
224(3)
Problems
227(6)
III Bifurcations, Chaotic Dynamics, Stochastic Models, and Discretization of Continuous Models
Deterministic and Stochastic Models in Applied Sciences
233(34)
Introduction
233(1)
Mathematical Modeling in Applied Sciences
234(5)
Examples of Mathematical Models
239(5)
Further Remarks on Modeling
244(2)
Mathematical Modeling and Stochasticity
246(17)
Random variables and stochastic calculus
251(8)
Moment representation of the dynamic response
259(2)
Statistical representation of large systems
261(2)
Problems
263(4)
Chaotic Dynamics, Stability, and Bifurcations
267(46)
Introduction
267(1)
Stability Diagrams
268(7)
Stability Diagrams and Potential Energy
275(7)
Limit Cycles
282(5)
Hopf Bifurcation
287(5)
Chaotic Motions
292(2)
Applications
294(15)
Ring on a rotating wire
294(4)
Metallic meter
298(3)
Line galloping model
301(3)
Flutter instability model
304(2)
Models presenting transition to chaos
306(3)
Problems
309(4)
Discrete Models of Continuous Systems
313(28)
Introduction
313(4)
Diffusion Models
317(4)
Mathematical Models of Traffic Flow
321(5)
Mathematical Statement of Problems
326(3)
Discretization of Continuous Models
329(7)
Problems
336(5)
Appendix I. Numerical Methods for Ordinary Differential Equations 341(16)
1 Introduction
341(1)
2 Numerical Methods for Initial-Value Problems
342(7)
3 Numerical Methods for Boundary-Value Problems
349(8)
Appendix II. Kinematics, Applied Forces, Momentum and Mechanical Energy 357(20)
1 Introduction
357(1)
2 Systems of Applied Forces
358(3)
3 Fundamental of Kinematics
361(2)
4 Center of Mass
363(2)
5 Tensor of Inertia
365(4)
6 Linear Momentum
369(1)
7 Angular Momentum
370(2)
8 Kinetic Energy
372(5)
Appendix III. Scientific Programs 377(32)
1 Introduction to Programming
377(5)
2 Scientific Programs
382(27)
References 409(2)
Subject Index 411