osculatingadj.

Brit.

/ˈɒskjᵿleɪtɪŋ/, U.S.

/ˈɑskjəˌleɪdɪŋ/

Origin: Formed within English, by derivation. Etymons: osculate v., -ing suffix².

Etymology: < osculate v. + -ing suffix².

That osculates (in various senses); (Geometry, of a curve or surface) that osculates another curve or surface.

ΘΚΠ

the world > relative properties > number > geometry > curve > [adjective] > osculating

osculatory1753

osculating1816

oscular1869

osculant1879

1816 tr. S. F. Lacroix Elem. Treat. Differential & Integral Calculus 108 This circle, called the osculating circle [Fr. cercle osculateur], will be the limit of all the others.

1866 J. Martineau Ess. 148 Two atoms unite, when, through rotation in opposite directions, their osculating surfaces are moving in the same.

1870 Amer. Naturalist 4 241 That grasses..vary much as other plants do, is plain from the multitude of osculating forms.

1923 Jrnl. Optical Soc. Amer. 7 197 Osculating paraboloids are..much closer approximations to the required aspheric surfaces than are the osculating spherical surfaces.

1972 M. Kline Math. Thought xxxv. 857 To the cusps there correspond osculating tangents (tangents which cross the curve at inflection points).

1993 Economist (Nexis) 10 July 22 The osculating couples in St James's Park.

Compounds

osculating circle n. Geometry a circle that osculates a curve at a given point, whose radius is the radius of curvature of the curve at that point.

ΚΠ

1816Osculating circle [see main sense].

1870 Proc. Royal Soc. 19 497 By inversion we get the characteristics for the osculating circles of bicircular quartics.

1984 W. Schofield Engin. Surveying (ed. 3) I. vi. 186 Before the angles to the osculating circle can be found the value of r₃ must be known.

osculating element n. Astronomy (usually in plural) an element of the data needed to determine the osculating ellipse of a celestial object.

ΚΠ

1868 J. C. Watson Theoret. Astron. (1964) viii. 459 The transformation from a system of osculating elements for one epoch to that for another epoch is very easily effected.

1905 Proc. Royal Soc. A. 76 269 The osculating elements referred to the epoch and mean equinox of November 14, 1905, are—M… 359° 2.4′… π… 109 17.1… Ω… 235 55.8… a… 3.5230.

1992 P. K. Seidelmann & G. A. Wilkins in P. K. Seidelmann Explanatory Suppl. Astron. Almanac i. 28 The elements may be given as osculating elements, which are the instantaneous values of the elements or the elements for the elliptical motion that the body would follow if perturbing effects were removed.

osculating ellipse n. Astronomy an ellipse that represents the orbital elements (element n. 7a) of a celestial object at a given moment but, because it does not allow for perturbation effects, differs from the actual orbit that the object will follow.

ΚΠ

1855 Philos. Trans. (Royal Soc.) 8 335 Thus the instantaneous ellipse, relatively to the moving axes, is of the same dimensions and in the same plane as the osculating ellipse; and it only remains to show that it coincides with the latter in position.

1907 Ann. Math. 8 145 As the eccentricity of the osculating ellipse seems to be of importance, it appears worthwhile to calculate the change of eccentricity during a revolution.

1988 A. E. Roy Orbital Motion (ed. 3) vi. 164 If the elements of the orbit (let it be an ellipse) are a₀, i₀, i₀, Ω₀, ω₀ and τ₀.., the ellipse with these elements is called the osculating ellipse while the elements are referred to as the osculating elements at time t₀.

osculating plane n. Geometry a plane that osculates a curve at a given point, which is spanned by the tangent and the principal normal at that point.

ΚΠ

a1832 Encycl. Metrop. (1845) II. 154 (heading) On the osculating plane of a curve of double curvature.

1865 Pall Mall Gaz. 25 May 1 Lord Granville..is, as it were, to use a mathematical metaphor, an osculating plane to all the different shades of aristocratic and cultivated liberalism.

1922 Trans. Amer. Math. Soc. 23 224 Their osculating planes form a pencil with the surface normal of P as axis.

1972 M. Kline Math. Thought xxiii. 562 John Bernoulli..wrote to Leibniz in 1698 to point out that the osculating plane (the plane of the osculating circle) at any point of a geodesic is perpendicular to the surface at that point.

This entry has been updated (OED Third Edition, September 2004; most recently modified version published online March 2022).

单词	osculating
释义	osculatingadj. Brit. /ˈɒskjᵿleɪtɪŋ/, U.S. /ˈɑskjəˌleɪdɪŋ/ Origin: Formed within English, by derivation. Etymons: osculate v., -ing suffix². Etymology: < osculate v. + -ing suffix². That osculates (in various senses); (Geometry, of a curve or surface) that osculates another curve or surface. ΘΚΠ the world > relative properties > number > geometry > curve > [adjective] > osculating osculatory1753 osculating1816 oscular1869 osculant1879 1816 tr. S. F. Lacroix Elem. Treat. Differential & Integral Calculus 108 This circle, called the osculating circle [Fr. cercle osculateur], will be the limit of all the others. 1866 J. Martineau Ess. 148 Two atoms unite, when, through rotation in opposite directions, their osculating surfaces are moving in the same. 1870 Amer. Naturalist 4 241 That grasses..vary much as other plants do, is plain from the multitude of osculating forms. 1923 Jrnl. Optical Soc. Amer. 7 197 Osculating paraboloids are..much closer approximations to the required aspheric surfaces than are the osculating spherical surfaces. 1972 M. Kline Math. Thought xxxv. 857 To the cusps there correspond osculating tangents (tangents which cross the curve at inflection points). 1993 Economist (Nexis) 10 July 22 The osculating couples in St James's Park. Compounds osculating circle n. Geometry a circle that osculates a curve at a given point, whose radius is the radius of curvature of the curve at that point. ΚΠ 1816Osculating circle [see main sense]. 1870 Proc. Royal Soc. 19 497 By inversion we get the characteristics for the osculating circles of bicircular quartics. 1984 W. Schofield Engin. Surveying (ed. 3) I. vi. 186 Before the angles to the osculating circle can be found the value of r₃ must be known. osculating element n. Astronomy (usually in plural) an element of the data needed to determine the osculating ellipse of a celestial object. ΚΠ 1868 J. C. Watson Theoret. Astron. (1964) viii. 459 The transformation from a system of osculating elements for one epoch to that for another epoch is very easily effected. 1905 Proc. Royal Soc. A. 76 269 The osculating elements referred to the epoch and mean equinox of November 14, 1905, are—M… 359° 2.4′… π… 109 17.1… Ω… 235 55.8… a… 3.5230. 1992 P. K. Seidelmann & G. A. Wilkins in P. K. Seidelmann Explanatory Suppl. Astron. Almanac i. 28 The elements may be given as osculating elements, which are the instantaneous values of the elements or the elements for the elliptical motion that the body would follow if perturbing effects were removed. osculating ellipse n. Astronomy an ellipse that represents the orbital elements (element n. 7a) of a celestial object at a given moment but, because it does not allow for perturbation effects, differs from the actual orbit that the object will follow. ΚΠ 1855 Philos. Trans. (Royal Soc.) 8 335 Thus the instantaneous ellipse, relatively to the moving axes, is of the same dimensions and in the same plane as the osculating ellipse; and it only remains to show that it coincides with the latter in position. 1907 Ann. Math. 8 145 As the eccentricity of the osculating ellipse seems to be of importance, it appears worthwhile to calculate the change of eccentricity during a revolution. 1988 A. E. Roy Orbital Motion (ed. 3) vi. 164 If the elements of the orbit (let it be an ellipse) are a₀, i₀, i₀, Ω₀, ω₀ and τ₀.., the ellipse with these elements is called the osculating ellipse while the elements are referred to as the osculating elements at time t₀. osculating plane n. Geometry a plane that osculates a curve at a given point, which is spanned by the tangent and the principal normal at that point. ΚΠ a1832 Encycl. Metrop. (1845) II. 154 (heading) On the osculating plane of a curve of double curvature. 1865 Pall Mall Gaz. 25 May 1 Lord Granville..is, as it were, to use a mathematical metaphor, an osculating plane to all the different shades of aristocratic and cultivated liberalism. 1922 Trans. Amer. Math. Soc. 23 224 Their osculating planes form a pencil with the surface normal of P as axis. 1972 M. Kline Math. Thought xxiii. 562 John Bernoulli..wrote to Leibniz in 1698 to point out that the osculating plane (the plane of the osculating circle) at any point of a geodesic is perpendicular to the surface at that point. This entry has been updated (OED Third Edition, September 2004; most recently modified version published online March 2022). < adj.1816
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