Abstract
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.
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Russian Text © The Author(s). 2019. published in Vestnik Moskovskogo Universiteta, Matematika, Mekhanika, 2019, Vol. 74, No. 4, pp. 15–27.
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Gerasimova, O.V., Razmyslov, Y.P. The Gravity First (on Reincarnation of Third Kepler’s Law). Moscow Univ. Math. Bull. 74, 147–158 (2019). https://doi.org/10.3103/S002713221904003X
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DOI: https://doi.org/10.3103/S002713221904003X