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Given the different Sun incidence in different positions in the orbit, it is necessary to define a standard point of the orbit of the planet, to define the planet position in the orbit at each moment of the year w.r.t such point; this point is called with several names: vernal equinox, spring equinox, March equinox, all equivalent, and named considering northern hemisphere seasons.
3D visualization of a sphere and a rotation about an Euler axis (^) by an angle of In 3-dimensional space, according to Euler's rotation theorem, any rotation or sequence of rotations of a rigid body or coordinate system about a fixed point is equivalent to a single rotation by a given angle about a fixed axis (called the Euler axis) that runs through the fixed point. [6]
A representation of rotations is a particular formalism, either algebraic or geometric, used to parametrize a rotation map. This meaning is somehow inverse to the meaning in the group theory. Rotations of (affine) spaces of points and of respective vector spaces are not always clearly distinguished.
Geometric transformations can be distinguished into two types: active or alibi transformations which change the physical position of a set of points relative to a fixed frame of reference or coordinate system (alibi meaning "being somewhere else at the same time"); and passive or alias transformations which leave points fixed but change the ...
Rotation period with respect to distant stars, the sidereal rotation period (compared to Earth's mean Solar days) Synodic rotation period (mean Solar day) Apparent rotational period viewed from Earth Sun [i] 25.379995 days (Carrington rotation) 35 days (high latitude) 25 d 9 h 7 m 11.6 s 35 d ~28 days (equatorial) [2] Mercury: 58.6462 days [3 ...
In mechanics and geometry, the 3D rotation group, often denoted SO(3), is the group of all rotations about the origin of three-dimensional Euclidean space under the operation of composition. [ 1 ] By definition, a rotation about the origin is a transformation that preserves the origin, Euclidean distance (so it is an isometry ), and orientation ...
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This is Rodrigues' formula for the axis of a composite rotation defined in terms of the axes of the two component rotations. He derived this formula in 1840 (see page 408). [3] The three rotation axes A, B, and C form a spherical triangle and the dihedral angles between the planes formed by the sides of this triangle are defined by the rotation ...