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Geometry of nonholonomically constrained systems /
This book gives a modern differential geometric treatment of linearly nonholonomically constrained systems. It discusses in detail what is meant by symmetry of such a system and gives a general theory of how to reduce such a symmetry using the concept of a differential space and the almost Poisson b...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New Jersey :
World Scientific,
©2010.
|
| Colección: | Advanced series in nonlinear dynamics ;
v. 26. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Nonholonomically constrained motions. Newton's equations
- Constraints
- Lagrange-d'Alembert equations
- Lagrange derivative
- Hamilton-d'Alembert equations
- Distributional Hamiltonian formulation
- Almost Poisson brackets
- Momenta and momentum equation
- Projection principle
- Accessible sets
- Constants of motion
- Notes
- Group actions and orbit spaces. Group actions
- Orbit spaces
- Isotropy and orbit types
- Smooth structure on an orbit space
- Subcartesian spaces
- Stratification of the orbit space by orbit types
- Derivations and vector fields on a differential space
- Vector fields on a stratified differential space
- Vector fields on an orbit space
- Tangent objects to an orbit space
- Notes
- Symmetry and reduction. Dynamical systems with symmetry
- Nonholonomic singular reduction
- Nonholonomic regular reduction
- Chaplygin systems
- Orbit types and reduction
- Conservation laws
- Lifted actions and the momentum equation
- Notes
- Reconstruction, relative equilibria and relative periodic orbits. Reconstruction
- Relative equilibria
- Relative periodic orbits
- Notes
- Carathéodory's sleigh. Basic set up
- Equations of motion
- Reduction of the E(2) symmetry
- Motion on the E(2) reduced phase space
- Reconstruction
- Notes
- Convex rolling rigid body. Basic set up
- Unconstrained motion
- Constraint distribution
- Constrained equations of motion
- Reduction of the translational [symbol] symmetry
- Reduction of E(2) symmetry
- Body of revolution
- Notes
- The rolling disk. General set up
- Reduction of the E(2) x S[symbol] symmetry
- Reconstruction
- Relative equilibria
- A potential function on an interval
- Scaling
- Solutions of the rescaled Chaplygin equations
- Bifurcations of a vertical disk
- The global geometry of the degeneracy locus
- Falling flat.
- Near falling flat
- The bifurcation diagram
- The integral map
- Constant energy slices
- The spatial rotational shift
- Notes.