Summary
The properties of a physical system Sk where k ≠−1, of ∞2n−1 trajectories C. in a Riemannian space Vn are developed. The intrinsic differential equations and the equations of Lagrange, of a physical system Sk, are derived. The Lagrangian function L and the Hamiltonian function H, are studied in the conservative case. Also included are systems of the type (G), curvature trajectories, and natural families. The Appell transformation T of a dynamical system S 0 in a Riemannian space Vn, is obtained. Finally, contact transformations and the transformation theory of a physical system Sk where k ≠−1, are considered in detail.
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References
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To Enrico Bompiani on his scientific Jubilee
Kasner,Differential geometric aspecte of dynamics, The Princeton Colloquium Lectures, 1909. Published by the « American Mathematical Society, Providence, Rhode Island, 1913, and reprinted 1934.
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De Cicco, J. The Riemannian geometry of physical systems of curves. Annali di Matematica 57, 339–403 (1962). https://doi.org/10.1007/BF02417748
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DOI: https://doi.org/10.1007/BF02417748