About four centuries ago, considering flat sections of cone x² + y² = z² (along the axis of revolution on the plane Oxy), Robert Hooke wrote one fundamental differential equation \((x,y,z)^{\prime\prime} = - {{4{\pi ^2}k} \over {{{(\sqrt {{x^2} + {y^2} + {z^2}})}^3}}}\; \cdot \;(x,y,z)\), which thereafter set the foundation of the law of universal gravitation and explanation of movement of charged particle in the classical stationary Coulomb field. In this paper, differential-algebraic models arising as the result of replacement of a cone by an arbitrary quadric surface F(x, y, z) = 0 with respect to (as we call it) the Kepler parametrization of quadratic curves {F(x, y, α · x + β · y + δ)=0 | α, β, δ ∈ K}, K = ℝ, ℂ, are proposed and studied.

中文翻译：

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重力优先（关于第三开普勒定律的轮回）

大约四个世纪前，考虑锥平坦区间X ² + Y ^ ² = Z ^ ²（沿平面上旋转轴氧），罗伯特·胡克写道：一个基本的微分方程\（（X，Y，Z）^ {\黄金\ prime} =-{{4 {\ pi ^ 2} k} \ over {{{（\ sqrt {{x ^ 2} + {y ^ 2} + {z ^ 2}}）} ^ 3}}} \; \ cdot \;（x，y，z）\），此后奠定了万有引力定律的基础，并解释了经典平稳库仑场中带电粒子的运动。在本文中，微分代数模型是由任意二次曲面F（x，y，z）关于二次曲线的开普勒参数化{ F（x，y，α · x +β · y +δ）= 0 |）= 0。提出并研究了α，β， δ∈K }，K＝K，ℝ。