國立虎尾科技大學 |

Inverse problems in ordinary differential equations and applications

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Inverse problems in ordinary differential equations and applications/ by Jaume Llibre, Rafael Ramirez.
作者:	Llibre, Jaume.
其他作者:	Ramirez, Rafael.
出版者:	Cham :Springer International Publishing : : 2016.,
面頁冊數:	xii, 266 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Inverse problems (Differential equations) -
電子資源:	http://dx.doi.org/10.1007/978-3-319-26339-7
ISBN:	9783319263397

Inverse problems in ordinary differential equations and applications
Llibre, Jaume.

Inverse problems in ordinary differential equations and applications[electronic resource] /by Jaume Llibre, Rafael Ramirez. - Cham :Springer International Publishing :2016. - xii, 266 p. :ill. (some col.), digital ;24 cm. - Progress in mathematics,v.3130743-1643 ;. - Progress in mathematics ;v.231..

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.

ISBN: 9783319263397

Standard No.: 10.1007/978-3-319-26339-7doiSubjects--Topical Terms:

528596
Inverse problems (Differential equations)

LC Class. No.: QA378.5

Dewey Class. No.: 515.357

Inverse problems in ordinary differential equations and applications
LDR:02439nam a2200325 a 4500 001 863210
003 DE-He213
005 20160922113044.0
006 m d
007 cr nn 008maaau
008 170720s2016 gw s 0 eng d
020 $a 9783319263397 $q (electronic bk.)
020 $a 9783319263373 $q (paper)
024 7 $a 10.1007/978-3-319-26339-7 $2 doi
035 $a 978-3-319-26339-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA378.5
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
082 0 4 $a 515.357 $2 23
090 $a QA378.5 $b .L791 2016
100 1 $a Llibre, Jaume. $3 1021384
245 1 0 $a Inverse problems in ordinary differential equations and applications $h [electronic resource] / $c by Jaume Llibre, Rafael Ramirez.
260 $a Cham : $c 2016. $b Springer International Publishing : $b Imprint: Birkhauser,
300 $a xii, 266 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Progress in mathematics, $x 0743-1643 ; $v v.313
505 0 $a 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.
520 $a 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.
650 0 $a Inverse problems (Differential equations) $3 528596
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Ordinary Differential Equations. $3 670854
700 1 $a Ramirez, Rafael. $3 1107058
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a Progress in mathematics ; $v v.231. $3 882991
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-26339-7
950 $a Mathematics and Statistics (Springer-11649)