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Changing orientation of a rigid body is the same as rotating the axes of a reference frame attached to it.. In geometry, the orientation, attitude, bearing, direction, or angular position of an object – such as a line, plane or rigid body – is part of the description of how it is placed in the space it occupies. [1]
A torus is an orientable surface The Möbius strip is a non-orientable surface. Note how the disk flips with every loop. The Roman surface is non-orientable.. In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "anticlockwise". [1]
The orientation of a real vector space or simply orientation of a vector space is the arbitrary choice of which ordered bases are "positively" oriented and which are "negatively" oriented. In the three-dimensional Euclidean space , right-handed bases are typically declared to be positively oriented, but the choice is arbitrary, as they may also ...
It is an important quantity in physics because it is a conserved quantity–that is, the total angular momentum of a closed system remains constant. angular velocity (ω) How fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.
Geometric terms of location describe directions or positions relative to the shape of an object. These terms are used in descriptions of engineering, physics, and other sciences, as well as ordinary day-to-day discourse. Though these terms themselves may be somewhat ambiguous, they are usually used in a context in which their meaning is clear.
In physics, this concept is applied to classical mechanics where rotational (or angular) kinematics is the science of quantitative description of a purely rotational motion. The orientation of an object at a given instant is described with the same tools, as it is defined as an imaginary rotation from a reference placement in space, rather than ...
The set of coordinates that define the position of a reference point and the orientation of a coordinate frame attached to a rigid body in three-dimensional space form its configuration space, often denoted () where represents the coordinates of the origin of the frame attached to the body, and () represents the rotation matrices that define the orientation of this frame relative to a ground ...
With these modern definitions, every geometric shape is defined as a set of points; this is not the case in synthetic geometry, where a line is another fundamental object that is not viewed as the set of the points through which it passes. However, there are modern geometries in which points are not primitive objects, or even without points.