[geocentrism] Re: Dual Axis Proof
- From: "philip madsen" <pma15027@xxxxxxxxxxxxxx>
- To: <geocentrism@xxxxxxxxxxxxx>
- Date: Sun, 4 Nov 2007 09:39:15 +1000
If as Neville and Paul say the Ecliptic axis is a real object and not a
subjective mathmatical/geometrical projection, may I ask which ecliptic of the
many the solar system has, including the invariable ecliptic plane is the real
one, and please tell me what makes it real. ?
Philip.
Laws.
Axis of rotation.
In mathematics:
a.. Coordinate axis, in mathematics, physics and engineering
b.. Axis of rotation, or axis of symmetry, in geometry-related contexts
A rotation is a movement of an object in a circular motion. A two-dimensional
object rotates around a center (or point) of rotation. A three-dimensional
object rotates around a line called an axis. If the axis of rotation is within
the body, the body is said to rotate upon itself, or spin—which implies
relative speed and perhaps free-movement with angular momentum. A circular
motion about an external point, e.g. the Earth about the Sun, is called an
orbit or more properly an orbital revolution.
Mathematically, a rotation is, unlike a translation, a rigid body movement
which keeps a point fixed. This definition applies to rotations within both two
and three dimensions (in a plane and in space, respectively.) A rotation in
three-dimensional space keeps an entire line fixed, i.e. a rotation in
three-dimensional space is a rotation around an axis. This follows from Euler's
rotation theorem.
In kinematics, Euler's rotation theorem states that, in three-dimensional
space, any displacement of a rigid body such that a point on the rigid body
remains fixed, is equivalent to a rotation about a fixed axis through that
point. The theorem is named after Leonhard Euler.
In mathematical terms, this is a statement that, in 3D space, any two
coordinate systems with a common origin are related by a rotation about some
fixed axis. This also means that the product of two rotation matrices is again
a rotation matrix. A (non-identity) rotation matrix has a real eigenvalue which
is equal to unity. The eigenvector corresponding to this eigenvalue is the axis
of rotation connecting the two systems.
All rigid body movements are rotations, translations, or combinations of the
two.
If a rotation around a point or axis is followed by a second rotation around
the same point/axis, a third rotation results. The reverse (inverse) of a
rotation is also a rotation. Thus, the rotations around a point/axis form a
group. However, a rotation around a point or axis and a rotation around a
different point/axis may result in something other than a rotation, e.g. a
translation.
The principal axes of rotation in space
Rotations around the x, y and z axes are called principal rotations. Rotation
around any axis can be performed by taking a rotation around the x axis,
followed by a rotation around the y axis, and followed by a rotation around the
z axis. That is to say, any spatial rotation can be decomposed into a
combination of principal rotations.
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