Thoan Do ; Geoff Prince
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The inverse problem in the calculus of variations: new developments
cm:9527 -
Communications in Mathematics,
April 30, 2021,
Volume 29 (2021), Issue 1 (Special Issue: Ostrava Mathematical Seminar)
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https://doi.org/10.2478/cm-2021-0008
The inverse problem in the calculus of variations: new developments
Authors: Thoan Do ; Geoff Prince
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Thoan Do;Geoff Prince
We deal with the problem of determining the existence and uniqueness of Lagrangians for systems of n second order ordinary differential equations. A number of recent theorems are presented, using exterior differential systems theory (EDS). In particular, we indicate how to generalise Jesse Douglas’s famous solution for n = 2. We then examine a new class of solutions in arbitrary dimension n and give some non-trivial examples in dimension 3.
On the inverse problem of the calculus of variations
2 Documents citing this article
Source : OpenCitations
Kruglikov, Boris, 0000-0001-5005-091; Matveev, Vladimir S., 2022, Almost Every Path Structure Is Not Variational, General Relativity And Gravitation, 54, 10, 10.1007/s10714-022-03006-2.
Prince, Geoff; Farré Puiggalí, M.; Saunders, D.J.; De Diego, D. Martín, 2021, Linear Connections And Shape Maps For Second Order ODEs With And Without Constraints, Journal Of Geometry And Physics, 170, pp. 104390, 10.1016/j.geomphys.2021.104390.