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The Gravity First (on Reincarnation of Third Kepler’s Law)
About four centuries ago, considering flat sections of cone x 2 + y 2 = z 2 (along the axis of revolution on the plane Oxy ), Robert Hooke wrote one fundamental differential equation ( x , y , z ) ″ = − 4 π 2 k ( x 2 + y 2 + z 2 ) 3 ⋅ ( x , y , z ) , which thereafter set the foundation of the law of...
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| Published in: | Moscow University mathematics bulletin 2019-07, Vol.74 (4), p.147-158 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| container_end_page | 158 |
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| container_title | Moscow University mathematics bulletin |
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| creator | Gerasimova, O. V. Razmyslov, Yu. P. |
| description | About four centuries ago, considering flat sections of cone
x
2
+
y
2
=
z
2
(along the axis of revolution on the plane
Oxy
), Robert Hooke wrote one fundamental differential equation
(
x
,
y
,
z
)
″
=
−
4
π
2
k
(
x
2
+
y
2
+
z
2
)
3
⋅
(
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. |
| doi_str_mv | 10.3103/S002713221904003X |
| format | article |
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x
2
+
y
2
=
z
2
(along the axis of revolution on the plane
Oxy
), Robert Hooke wrote one fundamental differential equation
(
x
,
y
,
z
)
″
=
−
4
π
2
k
(
x
2
+
y
2
+
z
2
)
3
⋅
(
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.</description><identifier>ISSN: 0027-1322</identifier><identifier>EISSN: 1934-8444</identifier><identifier>DOI: 10.3103/S002713221904003X</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Analysis ; Charged particles ; Differential equations ; Kepler laws ; Mathematics ; Mathematics and Statistics ; Parameterization</subject><ispartof>Moscow University mathematics bulletin, 2019-07, Vol.74 (4), p.147-158</ispartof><rights>Allerton Press, Inc. 2019</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c268t-488aab46199cca71a0b2272d2aefcf19294a64b5caebf81ddc5de75d4b7887e63</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Gerasimova, O. V.</creatorcontrib><creatorcontrib>Razmyslov, Yu. P.</creatorcontrib><title>The Gravity First (on Reincarnation of Third Kepler’s Law)</title><title>Moscow University mathematics bulletin</title><addtitle>Moscow Univ. Math. Bull</addtitle><description>About four centuries ago, considering flat sections of cone
x
2
+
y
2
=
z
2
(along the axis of revolution on the plane
Oxy
), Robert Hooke wrote one fundamental differential equation
(
x
,
y
,
z
)
″
=
−
4
π
2
k
(
x
2
+
y
2
+
z
2
)
3
⋅
(
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.</description><subject>Analysis</subject><subject>Charged particles</subject><subject>Differential equations</subject><subject>Kepler laws</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Parameterization</subject><issn>0027-1322</issn><issn>1934-8444</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1kMFKxDAURYMoOI5-gLuAG11Uk5e0TcCNDDOjWBB0BHflNU2dDrWtSUeZnb_h7_kldqjgQlw9Lveey-MScszZueBMXDwwBjEXAFwzyZh42iEjroUMlJRyl4y2drD198mB9yvGwlBLPiKXi6Wlc4dvZbehs9L5jp42Nb23ZW3Q1diVvWoKuliWLqe3tq2s-_r49DTB97NDsldg5e3Rzx2Tx9l0MbkOkrv5zeQqCQxEqgukUoiZjLjWxmDMkWUAMeSAtjAF16AlRjILDdqsUDzPTZjbOMxlFisV20iMycnQ27rmdW19l66adf9c5VMAJSAKpdJ9ig8p4xrvnS3S1pUv6DYpZ-l2pPTPSD0DA-P7bP1s3W_z_9A3zX5odw</recordid><startdate>20190701</startdate><enddate>20190701</enddate><creator>Gerasimova, O. V.</creator><creator>Razmyslov, Yu. P.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20190701</creationdate><title>The Gravity First (on Reincarnation of Third Kepler’s Law)</title><author>Gerasimova, O. V. ; Razmyslov, Yu. P.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-488aab46199cca71a0b2272d2aefcf19294a64b5caebf81ddc5de75d4b7887e63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Analysis</topic><topic>Charged particles</topic><topic>Differential equations</topic><topic>Kepler laws</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Parameterization</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gerasimova, O. V.</creatorcontrib><creatorcontrib>Razmyslov, Yu. P.</creatorcontrib><collection>CrossRef</collection><jtitle>Moscow University mathematics bulletin</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gerasimova, O. V.</au><au>Razmyslov, Yu. P.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Gravity First (on Reincarnation of Third Kepler’s Law)</atitle><jtitle>Moscow University mathematics bulletin</jtitle><stitle>Moscow Univ. Math. Bull</stitle><date>2019-07-01</date><risdate>2019</risdate><volume>74</volume><issue>4</issue><spage>147</spage><epage>158</epage><pages>147-158</pages><issn>0027-1322</issn><eissn>1934-8444</eissn><abstract>About four centuries ago, considering flat sections of cone
x
2
+
y
2
=
z
2
(along the axis of revolution on the plane
Oxy
), Robert Hooke wrote one fundamental differential equation
(
x
,
y
,
z
)
″
=
−
4
π
2
k
(
x
2
+
y
2
+
z
2
)
3
⋅
(
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.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.3103/S002713221904003X</doi><tpages>12</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0027-1322 |
| ispartof | Moscow University mathematics bulletin, 2019-07, Vol.74 (4), p.147-158 |
| issn | 0027-1322 1934-8444 |
| language | eng |
| recordid | cdi_proquest_journals_2283265489 |
| source | Springer Nature |
| subjects | Analysis Charged particles Differential equations Kepler laws Mathematics Mathematics and Statistics Parameterization |
| title | The Gravity First (on Reincarnation of Third Kepler’s Law) |
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