The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations, Issue 473
This monograph explores various aspects of the inverse problem of the calculus of variations for systems of ordinary differential equations. The main problem centres on determining the existence and degree of generality of Lagrangians whose system of Euler-Lagrange equations coicides with a given system of ordinary differential equations. The authors rederive the basic necessary and sufficient conditions of Douglas for second order equations and extend them to equations of higher order using methods of the variational bicomplex of Tulcyjew, Vinogradov, and Tsujishita. The authors present an algorithm, based upon exterior differential systems techniques, for solving the inverse problem for second order equations. a number of new examples illustrate the effectiveness of this approach.
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Selected Topics in the Geometrical Study of Differential Equations, Issue 96
Limited preview - 2002
3 FIRST INTEGRALS AND THE INVERSE PROBLEM FOR SECOND ORDER EQUATIONS
4 THE INVERSE PROBLEM FOR FOURTH ORDER ORDINARY DIFFERENTIAL EQUATIONS
5 EXTERIOR DIFFERENTIAL SYSTEMS AND THE INVERSE PROBLEM FOR SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS
7 THE INVERSE PROBLEM FOR TWO DIMENSIONAL SPRAYS
EDS and the Inverse Problem Geoff Prince, La Trobe University ...
EDS and the Inverse Problem. Geoff Prince, La Trobe University. August 21. st. , 2007. Bedlewo. Selected References. 1. je Aldridge. ...
www.impan.gov.pl/ ~jagrab/ prince-references.pdf
Transactions of the American Mathematical Society
I. Anderson and G. Thompson, The inverse problem of the calculus of variations for ordinary differential equations, Memoirs Amer. Math. Soc. 98 No. ...
www.ams.org/ tran/ 2002-354-07/ S0002-9947-02-02994-X/ home.html
The Integrability Conditions in the Inverse Problem of the ...
Acta Applicandae Mathematicae 54: 233–273, 1998. © 1998 Kluwer Academic Publishers. Printed in the Netherlands. 233. The Integrability Conditions in the ...
www.springerlink.com/ index/ J141W67XN8831H03.pdf
Crampin, Martínez, Sarlet: Linear connections for systems of ...
 I. ANDERSON and G. THOMPSON, The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations, Memoirs of the American Mathematical ...
www.numdam.org/ numdam-bin/ fitem?id=AIHPA_1996__65_2_223_0
The Inverse Problem of the Calculus of Variations for Sixth- and ...
Acta Applicandae Mathematicae 66: 25–39, 2001. © 2001 Kluwer Academic Publishers. Printed in the Netherlands. 25. The Inverse Problem of the Calculus of ...
www.springerlink.com/ index/ Q049788107R036U7.pdf
The Inverse Problem for Flat Kinetic Minus Potential Lagrangians
E. extracta mathematicae. Vol. 16, Num. 2, 241 – 248 (2001). The Inverse Problem for Flat Kinetic. Minus Potential Lagrangians. G. Thompson, ge Prince ...
www.unex.es/ extracta/ Vol-16-2/ 16a2thom.pdf