The theorem describes the following effect : rotation of an object about its first and third principal axes is stable, while rotation about its second principal axis ( or intermediate axis ) is not.
32.
By the principal axis theorem, the two eigenvectors of the matrix of the quadratic form of a central conic section ( ellipse or hyperbola ) are perpendicular ( major or minor axis of the conic.
33.
"' Canonical factor analysis "', also called Rao's canonical factoring, is a different method of computing the same model as PCA, which uses the principal axis method.
34.
"Ibarruri " has a notably slow rotation period of 140 hours, and seems to be in a non-principal axis rotation ( NPAR ), colloquially called as " tumbling ".
35.
Along the length of the river bank ran a long, broad street that was to become the main thoroughfare-Stirling Street-that was to be the principal axis for northern expansion of the city.
36.
In 1985 he demonstrated the tennis racket theorem, subsequently also called the " Dzhanibekov effect ", by showing that in free-fall rotation about an object's second principal axis is unstable.
37.
The concept was introduced by Leonhard Euler in his 1765 book " Theoria motus corporum solidorum seu rigidorum "; he discussed the moment of inertia and many related concepts, such as the principal axis of inertia.
38.
The simplest case to analyze is the one in which "'g "'is a principal axis ( eigenvector ) of \ varepsilon', and the other two eigenvalues of \ varepsilon'are identical.
39.
In monoclinic, rhombohedral, tetragonal, and trigonal / hexagonal systems there is one unique axis ( sometimes called the "'principal axis "') which has higher rotational symmetry than the other two axes.
40.
If L is aligned with a principal axis ( say x ) then it doesn't matter; L = I x ? and that doesn't change as the y and z axes rotate into each other.
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