Inverse problems in ordinary differential equations and applications [electronic resource] / Jaume Llibre, Rafael Ramírez.

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Inverse problems in ordinary differential equations and applications [electronic resource] / Jaume Llibre, Rafael Ramírez.

9783319263397 (electronic book)
3319263390 (electronic book)
9783319263373

Switzerland : Birkhäuser, 2016.

English

1 online resource (xii, 266 pages) : illustrations.

10.1007/978-3-319-26339-7 doi

QA378.5

515/.357

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 R̂N 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.

Includes bibliographical references and index.

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Online resource; title from PDF title page (SpringerLink, viewed March 15, 2016).

Progress in mathematics (Boston, Mass.) ; v. 313.

Print version: 9783319263373

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