Construct · 3 fields · 3 citations

Where does ellipsoid collide?

One name. Different field. Different construct. One map.

● jingle · one word, three constructs Nearest construct by meaning·not indexed
ellipsoid3 CONSTRUCTSInertia ellipsoidPOINSOT · INERTIAConfidence ellipsoidCOVARIANCE · REGIONReference ellipsoidGRS80 · DATUM SURFACE

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2002Inertia ellipsoid2002Confidence ellipsoid2012Reference ellipsoid
2026

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Classical mechanics

A quadric encoding a body's rotational inertia

In rigid-body mechanics the inertia ellipsoid (Poinsot's ellipsoid) is the quadric surface whose radius in any direction encodes the body's moment of inertia about an axis in that direction; its principal axes are the body's principal axes of inertia. Poinsot's construction then pictures torque-free rotation as this ellipsoid rolling without slipping on a fixed plane. Goldstein, Poole, and Safko's Classical mechanics develops both the ellipsoid and the construction. The referent is a quadric that represents how a body's rotational inertia is distributed in space.[1]

Unit
The principal moments of inertia, whose inverse square roots set the ellipsoid's semi-axes
Recovery means
Not applicable
Measured by
Found from the eigenvalues and eigenvectors of the body's inertia tensor

Multivariate statistics

An ellipsoidal region of plausible parameter values

In multivariate statistics a confidence (or concentration) ellipsoid is the ellipsoidal region in parameter space that, at a chosen confidence level, is expected to contain the true mean vector. Its centre is the sample mean, while its orientation and the lengths of its axes come from the covariance matrix, so strongly correlated variables yield a tilted, elongated ellipsoid. Johnson and Wichern's Applied multivariate statistical analysis derives it from the sampling distribution. The referent is a multidimensional uncertainty region, unrelated to a spinning body's inertia beyond the shared quadric shape.[2]

Unit
The region's axes, set by the covariance matrix and the confidence level
Recovery means
Not applicable
Measured by
Derived from the sample covariance and an F- or chi-square quantile for the chosen confidence level

Geodesy

The defined reference surface for coordinates

In geodesy the reference ellipsoid is the smooth mathematical surface of revolution (such as GRS80 or WGS84) chosen to approximate the Earth's figure and to serve as the surface on which latitude, longitude, and ellipsoidal height are defined. Geodetic coordinates are given relative to it, while the undulating geoid is measured as a separation from it. Torge and Müller's Geodesy specifies the common reference ellipsoids and their parameters. The referent is the defined ellipsoid of revolution used as a geodetic datum, a deliberate idealisation rather than a measured physical shape.[3]

Unit
The ellipsoid's semi-major axis and flattening
Recovery means
Not applicable
Measured by
Specified by its semi-major axis and flattening within a datum definition

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Nearby collisions

spheroid2 fields · 2 citationsjingle · one word, two constructsgeoid1 fields · 1 citationsanchor · a standalone construct

References

  1. Goldstein, H., Poole, C. P., & Safko, J. L. (2002). Classical mechanics (3rd ed.). Addison-Wesley. ISBN 9780201657029
  2. Johnson, R. A., & Wichern, D. W. (2002). Applied multivariate statistical analysis (5th ed.). Prentice Hall. ISBN 9780130925534
  3. Torge, W., & Müller, J. (2012). Geodesy (4th ed.). De Gruyter. ISBN 9783110207187

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