Alexander Mielke

(Author)

Hamiltonian and Lagrangian Flows on Center Manifolds: With Applications to Elliptic Variational Problems (1991)Paperback - 1991, 23 October 1991

Hamiltonian and Lagrangian Flows on Center Manifolds: With Applications to Elliptic Variational Problems (1991)
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Part of Series
Lecture Notes in Mathematics
Print Length
140 pages
Language
English
Publisher
Springer
Date Published
23 Oct 1991
ISBN-10
354054710X
ISBN-13
9783540547105

Description

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.

Product Details

Author:
Alexander Mielke
Book Edition:
1991
Book Format:
Paperback
Country of Origin:
DE
Date Published:
23 October 1991
Dimensions:
23.39 x 15.6 x 0.84 cm
ISBN-10:
354054710X
ISBN-13:
9783540547105
Language:
English
Location:
Berlin, Heidelberg
Pages:
140
Publisher:
Weight:
226.8 gm

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