Llibre / Ramírez Inverse Problems in Ordinary Differential Equations and Applications

1. Auflage 2016
ISBN: 978-3-319-26339-7
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 313, 266 Seiten, eBook

Reihe: Progress in Mathematics

This book is dedicated to study the inverse problem of ordinary differential equations, that is it focuses in finding all ordinary differential equations that satisfy a given set of properties. The Nambu bracket is the central tool in developing this approach. The authors start characterizing the ordinary differential equations in R^N which have a given set of partial integrals or first integrals. The results obtained are applied first to planar polynomial differential systems with a given set of such integrals, second to solve the 16th Hilbert problem restricted to generic algebraic limit cycles, third for solving the inverse problem for constrained Lagrangian and Hamiltonian mechanical systems, fourth for studying the integrability of a constrained rigid body. Finally the authors conclude with an analysis on nonholonomic mechanics, a generalization of the Hamiltonian principle, and the statement an solution of the inverse problem in vakonomic mechanics.

Zielgruppe

Research

Autoren/Hrsg.

Llibre, Jaume

Ramírez, Rafael

Inhaltsverzeichnis

Preface.- 1.Differential Equations with Given Partial and First Integrals.- 2.Polynomial Vector Fields with Given Partial and First Integrals.- 3.16th Hilbert Problem for Algebraic Limit Cycles.- 4.Inverse Problem for Constrained Lagrangian Systems.- 5.Inverse Problem for Constrained Hamiltonian Systems.- 6.Integrability of the Constrained Rigid Body.- 7.Inverse Problem in the Vakonomic Mechanics.- Index.- Bibliography.