Far Eastern Mathematical Journal

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Features of mappings leading to a central field


Guzev M.A.

2020, issue 1, . 5862
DOI: https://doi.org/10.47910/FEMJ202006


Abstract
For a mechanical system with two degrees of freedom, it is shown that the condition of zeroing the Jacobian map depended on the interaction potential selects a central field that ensures this condition fulfillment. It has been hypothesized that, in the general case, the features of coordinate mappings lead to potentials that admit the existence of an motion integral additional to the energy.

Keywords:
central field, motion integral

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References

[1] V.I. Arnol'd, Matematicheskie metody klassicheskoi mekhaniki, Editorial URSS, M., 2017.

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