Autonomous three-dimensional Newtonian systems which admit Lie and Noether point symmetries
Autonomous three-dimensional Newtonian systems which admit Lie and Noether point symmetries
复制标题
承认李点对称和诺特点对称的自治三维牛顿系统
DOI：
10.1088/1751-8113/45/27/275201
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
L. Karpathopoulos
中科院分区：
文献类型：
--
作者：
M. Tsamparlis;A. Paliathanasis;L. Karpathopoulos
我们确定了承认李点对称的三维自治牛顿系统和承认诺特点对称的三维自治牛顿哈密顿系统。我们应用这些结果来确定二维哈密顿动力系统，该系统在恒定的非零曲率空间中移动，并且可以通过诺特点对称性进行积分。结果的推导是几何的，可以自然地扩展到更高的维度。
We determine the autonomous three-dimensional Newtonian systems which admit Lie point symmetries and the three-dimensional autonomous Newtonian Hamiltonian systems which admit Noether point symmetries. We apply the results in order to determine the two-dimensional Hamiltonian dynamical systems which move in a space of constant non-vanishing curvature and are integrable via Noether point symmetries. The derivation of the results is geometric and can be extended naturally to higher dimensions.