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  2. Principal axis theorem - Wikipedia

    en.wikipedia.org/wiki/Principal_axis_theorem

    In geometry and linear algebra, a principal axis is a certain line in a Euclidean space associated with a ellipsoid or hyperboloid, generalizing the major and minor axes of an ellipse or hyperbola. The principal axis theorem states that the principal axes are perpendicular , and gives a constructive procedure for finding them.

  3. Semi-major and semi-minor axes - Wikipedia

    en.wikipedia.org/wiki/Semi-major_and_semi-minor_axes

    The semi-minor axis of an ellipse runs from the center of the ellipse (a point halfway between and on the line running between the foci) to the edge of the ellipse. The semi-minor axis is half of the minor axis. The minor axis is the longest line segment perpendicular to the major axis that connects two points on the ellipse's edge. The semi ...

  4. Ellipse - Wikipedia

    en.wikipedia.org/wiki/Ellipse

    An ellipse (red) obtained as the intersection of a cone with an inclined plane. Ellipse: notations Ellipses: examples with increasing eccentricity. In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.

  5. Kepler's laws of planetary motion - Wikipedia

    en.wikipedia.org/wiki/Kepler's_laws_of_planetary...

    The orbit of every planet is an ellipse with the sun at one of the two foci. Kepler's first law placing the Sun at one of the foci of an elliptical orbit Heliocentric coordinate system (r, θ) for ellipse. Also shown are: semi-major axis a, semi-minor axis b and semi-latus rectum p; center of ellipse and its two foci marked by

  6. Perimeter of an ellipse - Wikipedia

    en.wikipedia.org/wiki/Perimeter_of_an_ellipse

    An ellipse has two axes and two foci. Unlike most other elementary shapes, such as the circle and square, there is no algebraic equation to determine the perimeter of an ellipse. Throughout history, a large number of equations for approximations and estimates have been made for the perimeter of an ellipse.

  7. Ellipsoid - Wikipedia

    en.wikipedia.org/wiki/Ellipsoid

    Given: Ellipsoid ⁠ x 2 / a 2 ⁠ + ⁠ y 2 / b 2 ⁠ + ⁠ z 2 / c 2 ⁠ = 1 and the plane with equation n x x + n y y + n z z = d, which have an ellipse in common. Wanted: Three vectors f 0 (center) and f 1, f 2 (conjugate vectors), such that the ellipse can be represented by the parametric equation

  8. Poinsot's ellipsoid - Wikipedia

    en.wikipedia.org/wiki/Poinsot's_ellipsoid

    As described in the tennis racket theorem, rotation of an object around its first or third principal axis is stable, while rotation around its second principal axis (or intermediate axis) is not. The motion is simplified in the case of an axisymmetric body, in which the moment of inertia is the same about two of the principal axes.

  9. Principal axis - Wikipedia

    en.wikipedia.org/wiki/Principal_axis

    Principal axis may refer to: Principal axis (crystallography) Principal axis (mechanics) Principal axis theorem; See also. Aircraft principal axes;