In the paper, eight classes of integrable billiards are studied; in particular, classes introduced by the authors: elementary, topological, billiard books, billiards on the Minkowski plane, geodesic billiards on quadrics in three-dimensional Euclidean space, billiards in a magnetic field, and also a class containing all of the ones above. It turns out that, in the class of billiard books, topological obstacles to implementation occurred, for example, for the “twisted” Lagrange top (as we conventionally call a modification of the usual Lagrange top which we had discovered) for one of energy zones. We indicate this obstacle explicitly. It turns out further that this system can still be implemented in the class of magnetic billiards.

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通过具有势能和磁场的拓扑，测地台球实现可积分系统

本文研究了八类可集成台球。特别是由作者介绍的类：基础，拓扑，台球书，Minkowski平面上的台球，三维欧几里得空间中二次曲面上的测地线台球，磁场中的台球，以及包含上述所有这些的类。事实证明，在台球类中，例如，其中一个能量区的“扭曲”拉格朗日顶（通常称为对我们发现的常规拉格朗日顶的修改）发生了实施上的拓扑障碍。 。我们明确指出了这一障碍。进一步证明，该系统仍可以在电磁台球类中实现。