D. N. Goryachev的一个问题中的分离变量和第一积分的分支
The separation of variables and bifurcations of first integrals in one problem of D.N.Goryachev
摘要：
D. N. Goryachev在刚体动力学中的一个部分可积情形中的运动方程被变量的实变化分离。我们得到了在根式下具有六次多项式的Abel-Jacobi方程.自然相变量（动量和动量力的分量）通过初等代数函数中的分离变量显式表示。在此基础上，描述了系统的相拓扑。
英文摘要：
The equations of motion in one partial integrable case of D.N.Goryachev in the rigid body dynamics are separated by the real change of variables. We obtain the Abel--Jacobi equations with the polynomial of degree 6 under the radical. The natural phase variables (components of the momentum and the momentum force) are expressed via separated variables explicitly in elementary algebraic functions. Basing on these expressions the phase topology of the system is described.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
