Geometric approach to dynamics obtained by deformation of time-dependent Lagrangians. (English) Zbl 1349.53110
Summary: The relationship of equations of motion of a Lagrangian \(\phi (L)\) to those of \(L\) is studied in the non-autonomous case, and the question of the existence of a function \(\phi \) such that \(\phi (L)\) is dynamically equivalent to \(L\) is answered.
MSC:
| 53D12 | Lagrangian submanifolds; Maslov index |
| 53Z05 | Applications of differential geometry to physics |
| 70G45 | Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics |
| 70H03 | Lagrange’s equations |
Keywords:
non-standard Lagrangians; inverse problem; deformation of Lagrangians; equivalent deformationsReferences:
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