Dynamical Systems and Geometric Mechanics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Dynamical Systems and Geometric Mechanics write by Jared Maruskin. This book was released on 2018-08-21. Dynamical Systems and Geometric Mechanics available in PDF, EPUB and Kindle. Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explore similar systems that instead evolve on differentiable manifolds. The first part discusses the linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, Poincaré maps, Floquet theory, the Poincaré-Bendixson theorem, bifurcations, and chaos. The second part of the book begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms.
Introduction to Dynamical Systems and Geometric Mechanics
Introduction to Dynamical Systems and Geometric Mechanics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Dynamical Systems and Geometric Mechanics write by Jared M Maruskin. This book was released on 2016-02-01. Introduction to Dynamical Systems and Geometric Mechanics available in PDF, EPUB and Kindle. Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explores similar systems that instead evolve on differentiable manifolds. In the study of geometric mechanics, however, additional geometric structures are often present, since such systems arise from the laws of nature that govern the motions of particles, bodies, and even galaxies. In the first part of the text, we discuss linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, Poincare maps, Floquet theory, the Poincare-Bendixson theorem, bifurcations, and chaos. The second part of the text begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms. The final chapters cover Lagrangian and Hamiltonian mechanics from a modern geometric perspective, mechanics on Lie groups, and nonholonomic mechanics via both moving frames and fiber bundle decompositions. The text can be reasonably digested in a single-semester introductory graduate-level course. Each chapter concludes with an application that can serve as a springboard project for further investigation or in-class discussion. This is a color reprint of the first edition published in 2012."
Dynamical Systems
Dynamical Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Dynamical Systems write by Giuseppe Marmo. This book was released on 1985-12-23. Dynamical Systems available in PDF, EPUB and Kindle. In their discussion of the subject of classical mechanics, the authors of this book use a new and stimulating approach which involves looking at dynamical systems from the viewpoint of differential geometry.
Geometrical Theory of Dynamical Systems and Fluid Flows (revised Edition)
Geometrical Theory of Dynamical Systems and Fluid Flows (revised Edition) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometrical Theory of Dynamical Systems and Fluid Flows (revised Edition) write by . This book was released on 2009. Geometrical Theory of Dynamical Systems and Fluid Flows (revised Edition) available in PDF, EPUB and Kindle. "This is an introductory textbook on the geometrical theory of dynamical systems, fluid flows and certain integrable systems. The topics are interdisciplinary and extend from mathematics, mechanics and physics to mechanical engineering, and the approach is very fundamental. The main theme of this book is a unified formulation to understand dynamical evolutions of physical systems within mathematical ideas of Riemannian geometry and Lie groups by using well-known examples. Underlying mathematical concepts include transformation invariance, covariant derivative, geodesic equation and curvature tensors on the basis of differential geometry, theory of Lie groups and integrability. These mathematical theories are applied to physical systems such as free rotation of a top, surface wave of shallow water, action principle in mechanics, diffeomorphic flow of fluids, vortex motions and some integrable systems. In the latest edition, a new formulation of fluid flows is also presented in a unified fashion on the basis of the gauge principle of theoretical physics and principle of least action along with new type of Lagrangians. A great deal of effort has been directed toward making the description elementary, clear and concise, to provide beginners easy access to the topics."-
Geometric Control of Mechanical Systems
Geometric Control of Mechanical Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Control of Mechanical Systems write by Francesco Bullo. This book was released on 2019-06-12. Geometric Control of Mechanical Systems available in PDF, EPUB and Kindle. 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.
