Hamiltonian and Lagrangian Flows on Center Manifolds

with Applications to Elliptic Variational Problems
1991
ISBN: 978-3-540-54710-5
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1489, 140 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 248 g

Reihe: Lecture Notes in Mathematics

The theory of center manifold reduction is studied in this
monograph in the context of (infinite-dimensional) Hamil-
tonian and Lagrangian systems. The aim is to establish a
"natural reduction method" for Lagrangian systems to their
center manifolds. Nonautonomous problems are considered as
well assystems invariant under the action of a Lie group (
including the case of relative equilibria).
The theory is applied to elliptic variational problemson
cylindrical domains. As a result, all bounded solutions
bifurcating from a trivial state can be described by a
reduced finite-dimensional variational problem of Lagrangian
type. This provides a rigorous justification of rod theory
from fully nonlinear three-dimensional elasticity.
The book will be of interest to researchers working in
classical mechanics, dynamical systems, elliptic variational
problems, and continuum mechanics. It begins with the
elements of Hamiltonian theory and center manifold reduction
in order to make the methods accessible to non-specialists,
from graduate student level.

Zielgruppe

Research

Autoren/Hrsg.

Mielke, Alexander

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Vektoranalysis, Physikalische Felder
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung

Inhaltsverzeichnis

Notations and basic facts on center manifolds.- The linear theory.- Hamiltonian flows on center manifolds.- Hamiltonian systems with symmetries.- Lagrangian systems.- Nonautonomous systems.- Elliptic variational problems on cylindrical domains.- Capillarity surface waves.- Necking of strips.- Saint-Venant's problem.