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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Hamiltonian and Lagrangian Flows on Center Manifolds: With Applications to Elliptic Variational Problems

Hamiltonian and Lagrangian Flows on Center Manifolds: With Applications to Elliptic Variational Problems

Mielke, Alexander

Paperback

Series: Lecture Notes in Mathematics, Book 1489

General MathematicsPhysics

ISBN10: 354054710X
ISBN13: 9783540547105
Publisher: Springer
Published: Oct 23 1991
Pages: 140
Weight: 0.50
Height: 0.33 Width: 6.14 Depth: 9.21
Language: English
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.

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