Hamiltonian Structures and Generating Families

2012
ISBN: 978-1-4614-1498-8
Verlag: Springer

Buch, Englisch, 258 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 417 g

Reihe: Universitext

This book is an enhanced version of an earlier Russian edition. Besides thorough revisions, more emphasis was put on reordering the topics according to a category-theoretical view. This allows the mathematical results to be stated, proved, and understood in a much easier and elegant way.

Zielgruppe

Graduate

Autoren/Hrsg.

Benenti, Sergio

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Geometrie Geometrie der modernen Physik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Preface.- 1 Basic Notions of Calculus on Manifolds.- 2 Relations.- 3 Symplectic Relations on Symplectic Manifolds.- 4 Symplectic Relations on Cotangent Bundles.- 5 Canonical Lift on Cotangent Bundles.- 6 The Geometry of the Hamilton-Jacobi Equation.- 7 Hamiltonian Optics in Euclidean Spaces.- 8 Control of Static Systems.- 9 Supplementary Topics.- 10 Global Hamilton Principal Functions on S2 and H2.- References.- Index.

Über Autor(innen)

Benenti, Sergio
Sergio Benenti is a professor of mathematical physics at Università di Torino, Italy. His current fields of research include symplectic geometry with applications to physical theories, Riemannian geometry with applications to the theory of the separation of variables in the Hamilton-Jacobi equation and in other relevant differential equations of physics, and mathematical models of the dynamics of non-holonomic systems.

Sergio Benenti is a professor of mathematical physics at Università di Torino, Italy. His current fields of research include symplectic geometry with applications to physical theories, Riemannian geometry with applications to the theory of the separation of variables in the Hamilton-Jacobi equation and in other relevant differential equations of physics, and mathematical models of the dynamics of non-holonomic systems.