![]() ![]() The axis (where present) and the plane of a rotation are orthogonal.Ī representation of rotations is a particular formalism, either algebraic or geometric, used to parametrize a rotation map. Unlike the axis, its points are not fixed themselves. The plane of rotation is a plane that is invariant under the rotation.The axis of rotation is a line of its fixed points.The rotation group is a point stabilizer in a broader group of (orientation-preserving) motions. This (common) fixed point or center is called the center of rotation and is usually identified with the origin. The rotation group is a Lie group of rotations about a fixed point. These two types of rotation are called active and passive transformations. For example, in two dimensions rotating a body clockwise about a point keeping the axes fixed is equivalent to rotating the axes counterclockwise about the same point while the body is kept fixed. ![]() But in mechanics and, more generally, in physics, this concept is frequently understood as a coordinate transformation (importantly, a transformation of an orthonormal basis), because for any motion of a body there is an inverse transformation which if applied to the frame of reference results in the body being at the same coordinates. All rotations about a fixed point form a group under composition called the rotation group (of a particular space). Rotation can have a sign (as in the sign of an angle): a clockwise rotation is a negative magnitude so a counterclockwise turn has a positive magnitude.Ī rotation is different from other types of motions: translations, which have no fixed points, and (hyperplane) reflections, each of them having an entire ( n − 1)-dimensional flat of fixed points in a n- dimensional space. It can describe, for example, the motion of a rigid body around a fixed point. Any rotation is a motion of a certain space that preserves at least one point. Rotation in mathematics is a concept originating in geometry. Rotation of an object in two dimensions around a point O. JSTOR ( February 2014) ( Learn how and when to remove this template message).Unsourced material may be challenged and removed.įind sources: "Rotation" mathematics – news Please help improve this article by adding citations to reliable sources. This article needs additional citations for verification. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |