Inverse Problems in Ordinary Differential Equations and Applications (Progress in Mathematics (313))

Llibre, Jaume; Ramírez, Rafael

ISBN 10: 3319799355 / ISBN 13: 9783319799353

Published by Springer (India) Private Limited, 2018

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PRINT ON DEMAND pp. 278.

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Bibliographic Details

• Title: Inverse Problems in Ordinary Differential Equations and Applications (Progress in Mathematics (313))
• Publisher: Springer (India) Private Limited
• Publication Date: 2018
• Language: English
• ISBN 10: 3319799355
• ISBN 13: 9783319799353
• Binding: Soft cover
• Condition: New

About this title

Synopsis

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.