广义第四Appelrot类中的变量分离
Separation of variables in the generalized 4th Appelrot class
摘要：
我们认为类似的第四Appelrot类的运动的Kowalevski顶部的情况下，两个恒定的力场。这个族的轨迹充满了六维相空间中的四维曲面O^4。限制在这个曲面上的对合中的三个第一积分的常数填满了R^3中分歧图的一张图。我们指出这对部分积分，以获得显式的参数方程的这张。O^4上的诱导系统被证明是具有两个自由度的哈密顿系统，其诱导辛结构退化的点集很薄。给出了O^4上的分离变量和初相变量的代数公式。
英文摘要：
We consider the analogue of the 4th Appelrot class of motions of the Kowalevski top for the case of two constant force fields. The trajectories of this family fill the four-dimensional surface O^4 in the six-dimensional phase space. The constants of three first integrals in involution restricted to this surface fill one of the sheets of the bifurcation diagram in R^3. We point out the pair of partial integrals to obtain the explicit parametric equations of this sheet. The induced system on O^4 is shown to be Hamiltonian with two degrees of freedom having the thin set of points where the induced symplectic structure degenerates. The region of existence of motions in terms of the integral constants is found. We provide the separation of variables on O^4 and the algebraic formulae for the initial phase variables.
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