The integrability conditions in the inverse problem of the calculus of variations for second-order ordinary differential equations
- Author
- Willy Sarlet (UGent) , Michael Crampin (UGent) and E Martínez
- Organization
- Abstract
- A novel approach to a coordinate-free analysis of the multiplier question in the inverse problem of the calculus of variations, initiated in a previous publication, is completed in the following sense: under quite general circumstances, the complete set of passivity or integrability conditions is computed for systems with arbitrary dimension n. The results are applied to prove that the problem is always solvable in the case that the Jacobi endomorphism of the system is a multiple of the identity. This generalizes to arbitrary n a result derived by Douglas for n = 2.
- Keywords
- inverse problem, Lagrangian systems, integrability, TANGENT BUNDLE, DERIVATIONS, DYNAMICS, SYSTEMS, FORMS
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-174088
- MLA
- Sarlet, Willy, et al. “The Integrability Conditions in the Inverse Problem of the Calculus of Variations for Second-Order Ordinary Differential Equations.” ACTA APPLICANDAE MATHEMATICAE, vol. 54, no. 3, 1998, pp. 233–73, doi:10.1023/A:1006102121371.
- APA
- Sarlet, W., Crampin, M., & Martínez, E. (1998). The integrability conditions in the inverse problem of the calculus of variations for second-order ordinary differential equations. ACTA APPLICANDAE MATHEMATICAE, 54(3), 233–273. https://doi.org/10.1023/A:1006102121371
- Chicago author-date
- Sarlet, Willy, Michael Crampin, and E Martínez. 1998. “The Integrability Conditions in the Inverse Problem of the Calculus of Variations for Second-Order Ordinary Differential Equations.” ACTA APPLICANDAE MATHEMATICAE 54 (3): 233–73. https://doi.org/10.1023/A:1006102121371.
- Chicago author-date (all authors)
- Sarlet, Willy, Michael Crampin, and E Martínez. 1998. “The Integrability Conditions in the Inverse Problem of the Calculus of Variations for Second-Order Ordinary Differential Equations.” ACTA APPLICANDAE MATHEMATICAE 54 (3): 233–273. doi:10.1023/A:1006102121371.
- Vancouver
- 1.Sarlet W, Crampin M, Martínez E. The integrability conditions in the inverse problem of the calculus of variations for second-order ordinary differential equations. ACTA APPLICANDAE MATHEMATICAE. 1998;54(3):233–73.
- IEEE
- [1]W. Sarlet, M. Crampin, and E. Martínez, “The integrability conditions in the inverse problem of the calculus of variations for second-order ordinary differential equations,” ACTA APPLICANDAE MATHEMATICAE, vol. 54, no. 3, pp. 233–273, 1998.
@article{174088,
abstract = {{A novel approach to a coordinate-free analysis of the multiplier question in the inverse problem of the calculus of variations, initiated in a previous publication, is completed in the following sense: under quite general circumstances, the complete set of passivity or integrability conditions is computed for systems with arbitrary dimension n. The results are applied to prove that the problem is always solvable in the case that the Jacobi endomorphism of the system is a multiple of the identity. This generalizes to arbitrary n a result derived by Douglas for n = 2.}},
author = {{Sarlet, Willy and Crampin, Michael and Martínez, E}},
issn = {{0167-8019}},
journal = {{ACTA APPLICANDAE MATHEMATICAE}},
keywords = {{inverse problem,Lagrangian systems,integrability,TANGENT BUNDLE,DERIVATIONS,DYNAMICS,SYSTEMS,FORMS}},
language = {{eng}},
number = {{3}},
pages = {{233--273}},
title = {{The integrability conditions in the inverse problem of the calculus of variations for second-order ordinary differential equations}},
url = {{http://doi.org/10.1023/A:1006102121371}},
volume = {{54}},
year = {{1998}},
}
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