Billiards of Variable Configuration and Billiards with Slipping in Hamiltonian Geometry and Topologyстатья
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Дата последнего поиска статьи во внешних источниках: 20 февраля 2024 г.
Аннотация:A class of billiards is found, the geometry of which can change with a change in the energy of a ball moving on a ‘‘billiard table.’’ Such billiards are called force or evolutionary billiards. They make it possible to implement important integrable Hamiltonian systems (with two degrees of freedom) on the entire 4-dimensional phase space of the system at once. That is, simultaneously on all regular isoenergetic 3-dimensional surfaces. We have previously proven that force billiards implement the Euler and Lagrange integrable cases in the dynamics of a heavy body in 3-dimensional space. It is found that these two well-known systems are ‘‘billiard equivalent,’’ although they have integrals of different degrees—quadratic (Euler) and linear (Lagrange).