Mechanics and Dynamical Systems with Mathematica ®

✍ Scribed by Nicola Bellomo, Luigi Preziosi, Antonio Romano (auth.)

• Publisher: Birkhäuser Basel
• Year: 2000
• Tongue: English
• Leaves: 423
• Series: Modeling and Simulation in Science, Engineering and Technology
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xiii
Front Matter....Pages xv-xv
Models and Differential Equations....Pages 1-17
Models and Mathematical Problems....Pages 19-55
Stability and Perturbation Methods....Pages 57-90
Front Matter....Pages 91-91
Newtonian Dynamics....Pages 93-138
Rigid Body Dynamics....Pages 139-182
Energy Methods and Lagrangian Mechanics....Pages 183-230
Front Matter....Pages 231-231
Deterministic and Stochastic Models in Applied Sciences....Pages 233-265
Chaotic Dynamics, Stability, and Bifurcations....Pages 267-312
Discrete Models of Continuous Systems....Pages 313-339
Back Matter....Pages 341-417

✦ Subjects

Appl.Mathematics/Computational Methods of Engineering; Dynamical Systems and Ergodic Theory; Computational Intelligence