Inverse Problems in Ordinary Differential Equations and Applications. 1st ed. 2016

種類:

電子ブック

責任表示:

by Jaume Llibre, Rafael Ramírez

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2016

著者名:

• Llibre, Jaume.
• Ramírez, Rafael.
• SpringerLink (Online service)

シリーズ名:

Progress in Mathematics ; 313

ISBN:

9783319263397 [3319263390]    

注記:

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.
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.

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