Geometry of Nonholonomically Constrained Systems

Geometry of Nonholonomically Constrained Systems
Author :
Publisher : World Scientific
Total Pages : 421
Release :
ISBN-10 : 9789814289498
ISBN-13 : 9814289493
Rating : 4/5 (98 Downloads)

Book Synopsis Geometry of Nonholonomically Constrained Systems by : Richard H. Cushman

Download or read book Geometry of Nonholonomically Constrained Systems written by Richard H. Cushman and published by World Scientific. This book was released on 2010 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Nonholonomically constrained motions. 1.1. Newton's equations. 1.2. Constraints. 1.3. Lagrange-d'Alembert equations. 1.4. Lagrange derivative. 1.5. Hamilton-d'Alembert equations. 1.6. Distributional Hamiltonian formulation. 1.7. Almost Poisson brackets. 1.8. Momenta and momentum equation. 1.9. Projection principle. 1.10. Accessible sets. 1.11. Constants of motion. 1.12. Notes -- 2. Group actions and orbit spaces. 2.1. Group actions. 2.2. Orbit spaces. 2.3. Isotropy and orbit types. 2.4. Smooth structure on an orbit space. 2.5. Subcartesian spaces. 2.6. Stratification of the orbit space by orbit types. 2.7. Derivations and vector fields on a differential space. 2.8. Vector fields on a stratified differential space. 2.9. Vector fields on an orbit space. 2.10. Tangent objects to an orbit space. 2.11. Notes -- 3. Symmetry and reduction. 3.1. Dynamical systems with symmetry. 3.2. Nonholonomic singular reduction. 3.3. Nonholonomic regular reduction. 3.4. Chaplygin systems. 3.5. Orbit types and reduction. 3.6. Conservation laws. 3.7. Lifted actions and the momentum equation. 3.8. Notes -- 4. Reconstruction, relative equilibria and relative periodic orbits. 4.1. Reconstruction. 4.2. Relative equilibria. 4.3. Relative periodic orbits. 4.4. Notes -- 5. Carathéodory's sleigh. 5.1. Basic set up. 5.2. Equations of motion. 5.3. Reduction of the E(2) symmetry. 5.4. Motion on the E(2) reduced phase space. 5.5. Reconstruction. 5.6. Notes -- 6. Convex rolling rigid body. 6.1. Basic set up. 6.2. Unconstrained motion. 6.3. Constraint distribution. 6.4. Constrained equations of motion. 6.5. Reduction of the translational [symbol] symmetry. 6.6. Reduction of E(2) symmetry. 6.7. Body of revolution. 6.8. Notes -- 7. The rolling disk. 7.1. General set up. 7.2. Reduction of the E(2) x S[symbol] symmetry. 7.3. Reconstruction. 7.4. Relative equilibria. 7.5. A potential function on an interval. 7.6. Scaling. 7.7. Solutions of the rescaled Chaplygin equations. 7.8. Bifurcations of a vertical disk. 7.9. The global geometry of the degeneracy locus. 7.10. Falling flat. 7.11. Near falling flat. 7.12. The bifurcation diagram. 7.13. The integral map. 7.14. Constant energy slices. 7.15. The spatial rotational shift. 7.16. Notes.


Geometry of Nonholonomically Constrained Systems Related Books

Geometry of Nonholonomically Constrained Systems
Language: en
Pages: 421
Authors: Richard H. Cushman
Categories: Mathematics
Type: BOOK - Published: 2010 - Publisher: World Scientific

DOWNLOAD EBOOK

1. Nonholonomically constrained motions. 1.1. Newton's equations. 1.2. Constraints. 1.3. Lagrange-d'Alembert equations. 1.4. Lagrange derivative. 1.5. Hamilton-
Nonholonomic Mechanics and Control
Language: en
Pages: 498
Authors: A.M. Bloch
Categories: Mathematics
Type: BOOK - Published: 2008-02-03 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

This book explores connections between control theory and geometric mechanics. The author links control theory with a geometric view of classical mechanics in b
Geometry of Nonholonomically Constrained Systems
Language: en
Pages: 421
Authors: Richard H. Cushman
Categories: Mathematics
Type: BOOK - Published: 2010 - Publisher: World Scientific

DOWNLOAD EBOOK

This book gives a modern differential geometric treatment of linearly nonholonomically constrained systems. It discusses in detail what is meant by symmetry of
Nonholonomic Mechanics and Control
Language: en
Pages: 501
Authors: A.M. Bloch
Categories: Mathematics
Type: BOOK - Published: 2007-09-27 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

This book explores connections between control theory and geometric mechanics. The author links control theory with a geometric view of classical mechanics in b
The Breadth of Symplectic and Poisson Geometry
Language: en
Pages: 666
Authors: Jerrold E. Marsden
Categories: Mathematics
Type: BOOK - Published: 2007-07-03 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

* The invited papers in this volume are written in honor of Alan Weinstein, one of the world’s foremost geometers * Contributions cover a broad range of topic