مجسم كروي

(تم التحويل من Spheroid)
OblateSpheroid.PNG
ProlateSpheroid.png
كروي مفلطح كروي متطاول

الجسم شبه الكروي (البيضاوي) Spheroid، هو جسم ناتج من تدوير قطع ناقص ( أهليلج ) حول أحد محاوره.

فمثلا البيضة هي من الأجسام شبه الكروية، غير المنتظمة.

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المعادلة

The assignment of semi-axes on a spheroid. Ii is oblate if c<a and prolate if c>a.

The equation of a tri-axial ellipsoid centred at the origin with semi-axes a,b, c aligned along the coordinate axes is

The equation of a spheroid with Oz as the symmetry axis is given by setting a=b:

The semi-axis a is the equatorial radius of the spheroid, and c is the distance from centre to pole along the symmetry axis. There are two possible cases:

  •   c < a  :  oblate spheroid
  •   c > a  :  prolate spheroid

The case of a=c reduces to a sphere.


المساحة

An oblate spheroid with c < a has surface area

The oblate spheroid is generated by rotation about the Oz axis of an ellipse with semi-major axis a and semi-minor axis c, therefore e may be identified as the eccentricity. (See ellipse). A derivation of this result may be found at.[1]

A prolate spheroid with c > a has surface area

The prolate spheroid is generated by rotation about the Oz axis of an ellipse with semi-major axis c and semi-minor axis a, therefore e may again be identified as the eccentricity. (See ellipse). A derivation of this result may be found at.[2]


الحجم

The volume inside a spheroid (of any kind) is . If A=2a is the equatorial diameter, and C=2c is the polar diameter, the volume is .

الانحناء

If a spheroid is parameterized as

where is the reduced or parametric latitude, is the longitude, and and , then its Gaussian curvature is

and its mean curvature is

Both of these curvatures are always positive, so that every point on a spheroid is elliptic.

انظر أيضاً

الهامش

  1. ^ "Oblate Spheroid - from Wolfram MathWorld". Mathworld.wolfram.com. Retrieved 2014-06-24. 
  2. ^ "Prolate Spheroid - from Wolfram MathWorld". Mathworld.wolfram.com. 2003-10-07. Retrieved 2014-06-24.