Types of Coordinate System
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
Another common coordinate system for the plane is the polar coordinate system. A point is chosen as the pole and a ray from this point is taken as the polar axis. For a given angle θ, there is a single line through the pole whose angle with the polar axis is θ (measured counterclockwise from the axis to the line).
These cylindrical and spherical coordinate systems do not move together with the body: they are steady, just like the cartesian system of coordinates. You set up the system with its axes, and describe the motion of the body with respect the fixed axes of the system. The body can have acceleration in any direction, x, y, z. In the same way, it can have acceleration along the circles ...
Homogeneous Coordinates . One of the many purposes of using homogeneous coordinates is to capture the concept of infinity. In the Euclidean coordinate system, infinity is something that does not exist. Mathematicians have discovered that many geometric concepts and computations can be greatly simplified if the concept of infinity is used.
A coordinate system is a two-dimensional number line, for example, two perpendicular number lines or axes. This is a typical coordinate system: The horizontal axis is called the x-axis and the vertical axis is called the y-axis. The center of the coordinate system (where the lines intersect) is called the origin.
In general, a homogeneous coordinate system is one where only the ratios of the coordinates are significant and not the actual values. Other commonly used systems. Some other common coordinate systems are the following: Curvilinear coordinates are a generalization of coordinate systems generally; the system is based on the intersection of curves.
Points in the polar coordinate system with pole O and polar axis L. In green, the point with radial coordinate 3 and angular coordinate 60 degrees or (3, 60°). In blue, the point (4, 210°).
Another common coordinate system for the plane is the polar coordinate system. A point is chosen as the pole and a ray from this point is taken as the polar axis. For a given angle θ, there is a single line through the pole whose angle with the polar axis is θ (measured counterclockwise from the axis to the line).