| Communications in Mathematics |
Thoan Do ; Geoff Prince - 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) - https://doi.org/10.2478/cm-2021-0008The inverse problem in the calculus of variations: new developmentsArticle
Authors: 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.
Source: HAL:hal-03665010v1
Volume: Volume 29 (2021), Issue 1 (Special Issue: Ostrava Mathematical Seminar)
Published on: April 30, 2021
Imported on: May 11, 2022
Keywords: [MATH]Mathematics [math]
Classifications
Mathematics Subject Classification 20201
- 37J06 - General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants
- 37J51 - Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods
- 49N45 - Inverse problems in optimal control
- 58A15 - Exterior differential systems (Cartan theory)
- 70H03 - Lagrange's equations
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