Inverse Problems in Ordinary Differential Equations and Applications

Jaume Llibre, Rafael Ramírez

ISBN 10: 3319263374 / ISBN 13: 9783319263373

Editore: Birkhauser Verlag AG, CH, 2016

Riguardo questo articolo

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.

Codice articolo LU-9783319263373

Dati bibliografici

• Titolo: Inverse Problems in Ordinary Differential Equations and Applications
• Editore: Birkhauser Verlag AG, CH
• Data di pubblicazione: 2016
• Lingua: Inglese
• ISBN 10: 3319263374
• ISBN 13: 9783319263373
• Rilegatura: Hardback
• Edizione: 1st ed. 2016.
• Condizione: New

Descrizione articolo

Riassunto

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.