Geometric Control of Mechanical Systems: Modeling, Analysis, and Design for Simple Mechanical Control Systems (Texts in Applied Mathematics) Review

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(More customer reviews)This is a very well written book on a difficult subject. A thorough study of "simple mechanical control systems" needs a background in Differential Geometry and students are faced with a great challenge in finding good references. Lewis and Bullo take that challenge and deliver this profoundly useful text. This book provides excellent chapters on the relavent concepts in basic algebra, differential geometry and Lie algebra. Then it introdues the simple mechanical systems in a very readable way. Concepts such as the configuration manifold, rigid bodies, kinetic energy, Riemannian metric etc are well explained in a general setting that the reader can draw analogies to Newtonian mechanics in Euclidean space. Book further discusses more advance topics such as Stability, Controllability and Perturbation analysis etc in Part II. Part III discusses design methodologies. There are plenty of exercises in the book and the website is very resourceful with supplementary material. This is a great addition to the collection of books by Abraham, Marsden, Arnol'd etc, and a must have for all graduate students working on this area.

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The area of analysis and control of mechanical systems using differential geometry is flourishing. This book collects many results over the last decade and provides a comprehensive introduction to the area.

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Mathematical Modeling and Simulation: Introduction for Scientists and Engineers Review

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(More customer reviews)This is a good an interesting book. I particularly like the author's focus on the basic concepts and philosophy of modelling as well as the use of open source software as Maxima. The book is clearly intended for beginners, like students at early university courses. I have only two negative comments on this book. One is that there is no chapter or section on dimensional analysis and scaling. The second, and more important is the high price, which is a hinder to the supposed intended audience.

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This concise and clear introduction to the topic requires only basic knowledge of calculus and linear algebra—all other concepts and ideas are developed in the course of the book. Lucidly written so as to appeal to undergraduates and practitioners alike, it enables readers to set up simple mathematical models on their own and to interpret their results and those of others critically. To achieve this, many examples have been chosen from various fields, such as biology, ecology, economics, medicine, agricultural, chemical, electrical, mechanical and process engineering, which are subsequently discussed in detail.
Based on the author's modeling and simulation experience in science and engineering and as a consultant, the book answers such basic questions as: What is a mathematical model? What types of models do exist? Which model is appropriate for a particular problem? What are simulation, parameter estimation, and validation?

The book relies exclusively upon open-source software which is available to everybody free of charge. The entire book software—including 3D CFD and structural mechanics simulation software—can be used based on a free CAELinux-Live-DVD that is available in the Internet (works on most machines and operating systems).

„...Very solid introductory text at the undergraduate level aimed at wide audience. Perfectly fits introductory modeling courses at colleges and universities that prefer to use opensource software rather than commercial one, and is an enjoyable reading in the first place. Highly recommended both as a main text and a supplementary one..."Yuri V. Rogovchenko (University of Kalmar, Sweden) in: Zentralblatt MATH (European Mathematical Society)

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Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers Review

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(More customer reviews)I most value this book for its brief and lucid introductions to the physics (e.g. multiphase flows) that can be incorporated into lattice Boltzmann methods.
As far as the lattice Boltzmann method is concerned, I soon found myself relying on papers in literature rather than this book (although it has to be said that this book thoroughly references publications in literature).
My main criticisms arise from following points:
* as a quick start guide, this book falls short in not discussing issues like initialisation and the general streaming-collision framework. I found the latter particularly confusing, since their code snippets suggest that they solve a slightly different equation than the one analytically described in the book. Moreover, the extension from 2D to 3D (which is left to the reader) is not as trivial as the book suggests (e.g. for the boundary conditions).
* the book gives an introduction to phenomenological models for e.g. multiphase flows. If you are an engineer or geoscientist, you might want to use models that are quantitatively more correct.
* The book doesn't go beyond lattice-Boltzmann toy models. If you want to do something "real" with lattice-Boltzmann, you will need to address more advanced issues (like how to deal with curved boundaries, or with higher-order lattices). While one cannot expect from the scope of this book to address those issues directly, it is a pity that the book doesn't prepare in any way for those issues. So probably, you'll have to throw away your code and start all over again if you ever want to model something more.
* Due to ongoing research, this book starts to become outdated. In part because the book introduces lattice-Boltzmann models from lattice-gas cellular automata (as they evolved historically), instead of being directly based on the Boltzmann transport equation (as is more common nowadays).
Overall, I quickly abandoned this book while writing my lattice-Boltzmann code. Nevertheless, you can probably have a lot of fun with the models proposed in the book, as long as you don't want to do anything too useful with it.


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Here is a basic introduction to Lattice Boltzmann models that emphasizes intuition and simplistic conceptualization of processes, while avoiding the complex mathematics that underlies LB models. The model is viewed from a particle perspective where collisions, streaming, and particle-particle/particle-surface interactions constitute the entire conceptual framework. Beginners and those whose interest is in model application over detailed mathematics will find this a powerful 'quick start' guide. Example simulations, exercises, and computer codes are included.

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A First Course in Mathematical Modeling Review

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(More customer reviews)From discrete to continuous modelling, with many proyects and examples, I like very spacially this book for the undergraduate level. The presentation is very clear, but rigurous, making experience the reader through the models. It focuses on the interpretation and ends with some tools for modelbuilding. For a start of mathematical model understanding of reality this book is specially good, clear and completely well written. Good job Mr. Giordano and Weir! See also: Mesterton-Gibbons:An aproach to Mathematical Modelling, Fowler: Mathematical Models in the Sciences, Beltrami: Mathematics for Dynamical Modeling, Morrison: The Art of Modeling Dynamical Systams and Giordano: Differential Equations a Modeling Aproach.

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Offering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 4th Edition delivers an excellent balance of theory and practice, and gives you relevant, hands-on experience developing and sharpening your modeling skills. Throughout, the book emphasizes key facets of modeling, including creative and empirical model construction, model analysis, and model research, and provides myriad opportunities for practice. The authors apply a proven six-step problem-solving process to enhance your problem-solving capabilities -- whatever your level. In addition, rather than simply emphasizing the calculation step, the authors first help you learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving you in the mathematical process as early as possible -- beginning with short projects -- this text facilitates your progressive development and confidence in mathematics and modeling.

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