Geodesic
Generating functions of the Cauchy operator of a hamiltonian system
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 19 (2023) no. 4, pp. 522-528

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The article is related to the mathematical apparatus for describing the phase trajectories of a hamiltonian system. An approach related to the construction of generating functions for the Cauchy operator is proposed. It is shown that one-parameter families of generating functions satisfy the Hamilton — Jacobi equation or its modifications. Using the example of small oscillations of a mathematical pendulum, it is shown that the description of the Cauchy operator for sufficiently long periods of time requires the use of generating functions of various types. With the help of generating functions, a variational principle similar to the principle of least action is formulated. The efficiency of using generating functions in the development of conservative methods of numerical integration is also noted.
Keywords: hamilton equations, generating function, Cauchy operator, variational principle. 
@article{VSPUI_2023_19_4_a7,
     author = {A. S. Shmyrov and V. A. Shmyrov and D. V. Shymanchuk},
     title = {Generating functions of the {Cauchy} operator of a hamiltonian system},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {522--528},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2023_19_4_a7/}
}
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A. S. Shmyrov; V. A. Shmyrov; D. V. Shymanchuk. Generating functions of the Cauchy operator of a hamiltonian system. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 19 (2023) no. 4, pp. 522-528. http://geodesic.mathdoc.fr/item/VSPUI_2023_19_4_a7/