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

Llibre, Jaume; Ramírez, Rafael

Hardcover

ISBN 10: 3319263374 ISBN 13: 9783319263373

Verlag: Birkhäuser, 2016

Inhaltsangabe

<P>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.</P>

Über diesen Titel

Críticas

“The book presents a new approach to ... inverse problems, where the authors mainly use as an essential tool the Nambu bracket. They deduce new properties of this bracket, which plays a fundamental role in the proof of all the results and in their applications throughout the book. ... The book is well written and contains new and valuable results in the development of the inverse problem in ordinary differential equations and its applications.” (Leonardo Colombo, Mathematical Reviews, January, 2017)

Reseña del editor

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.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2016
• ISBN 10: 3319263374
• ISBN 13: 9783319263373
• Einband: Tapa dura
• Sprache: Englisch
• Auflage: 1
• Anzahl der Seiten: 280