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Hipparchus. The concepts of angle and radius were already used by ancient peoples of the first millennium BC.The Greek astronomer and astrologer Hipparchus (190–120 BC) created a table of chord functions giving the length of the chord for each angle, and there are references to his using polar coordinates in establishing stellar positions. [2]
A robotic arm is a type of mechanical arm, usually programmable, with similar functions to a human arm; the arm may be the sum total of the mechanism or may be part of a more complex robot. The links of such a manipulator are connected by joints allowing either rotational motion (such as in an articulated robot ) or translational (linear ...
In green, the point with radial coordinate 3 and angular coordinate 60 degrees or (3,60°). In blue, the point (4,210°). By measuring bearings and distances, local polar coordinates are recorded. The orientation of this local polar coordinate system is defined by the 0° horizontal circle of the total station (polar
Let (x, y, z) be the standard Cartesian coordinates, and (ρ, θ, φ) the spherical coordinates, with θ the angle measured away from the +Z axis (as , see conventions in spherical coordinates). As φ has a range of 360° the same considerations as in polar (2 dimensional) coordinates apply whenever an arctangent of it is taken. θ has a range ...
A pendulum-driven spherical mobile robot. (The white arrow is used to determine the position and orientation of the robot via a vision-based algorithm.) A spherical robot, also known as spherical mobile robot, or ball-shaped robot is a mobile robot with spherical external shape. [1]
Complex numbers are often represented in polar form to aid calculations, and calculus can be applied to polar equations as well.The polar coordinate system is used in navigation, and polar coordinates extended into three dimensions are the basis for the earth's latitude and longitude system.The polar coordinate system can be applied anytime ...
This example employs polar coordinates, but more generally the added terms depend upon which coordinate system is chosen (that is, polar, elliptic, or any other system). Sometimes these coordinate-system dependent terms also are referred to as "fictitious forces", introducing a second meaning for "fictitious forces", despite the fact that these ...
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 ...