Some Applications of Affine in Velocities Lagrangians in Two-dimensional Systems

José F. Cariñena, José Fernández Núñez

Publication date: 25 November 2022

Abstract: The 2-dimensional inverse problem for first-order systems is analysed and a method to construct an affine Lagrangian for such systems is developed. The determination of such Lagrangians is based on the theory of the Jacobi multiplier for the system of differential equations. We illustrate our analysis with several examples of families of forces that are relevant in mechanics, on one side, and of some relevant biological systems, on the other.

Mathematics Subject Classification ID

Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Inverse problems for systems of particles (70F17) Lagrange's equations (70H03)

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