Lines of longitude are like the wedges of an orange, measured radially from a vertical line of symmetry connecting the poles. The slice at the Equator is at 0° latitude and the poles are at ☙0°.
Lines of latitude are horizontal slices through the globe. The distances between lines on the grid are not measured in miles or kilometres, but in degrees and minutes. The most familiar application of spherical coordinates is the system of latitude and longitude that divides the Earth’s surface into a grid for navigational purposes. Latitude and Longitude, Maps and Navigation If you make \(\phi\) a constant, you have a horizontal plane (or a cone).If you make \(\theta\) a constant, you have a vertical plane.If you make \(\rho\) a constant, you have a sphere.In an electrical context, polar coordinates are used in the design of applications using alternating current audio technicians use them to describe the ‘pick-up area’ of microphones and they are used in the analysis of temperature and magnetic fields. Examples include orbital motion, such as that of the planets and satellites, a swinging pendulum or mechanical vibration. Physicists and engineers use polar coordinates when they are working with a curved trajectory of a moving object (dynamics), and when that movement is repeated back and forth (oscillation) or round and round (rotation).
These could be anything from pressure vessels containing liquified gases to the many examples of dome structures in ancient and modern architectural masterpieces. Physically curved forms or structures include discs, cylinders, globes or domes. You may need to use polar coordinates in any context where there is circular, spherical or cylindrical symmetry in the form of a physical object, or some kind of circular or orbital (oscillatory) motion. However, two-dimensional polar coordinates and their three-dimensional relatives are used in a wide range of applications from engineering and aviation, to computer animation and architecture. In everyday situations, it is much more likely that you will encounter Cartesian coordinate systems than polar, spherical or cylindrical. Why are Polar, Spherical and Cylindrical Coordinates Important? Here, Cartesian coordinates are difficult to use and it becomes necessary to use a system derived from circular shapes, such as polar, spherical or cylindrical coordinate systems. However, some applications involve curved lines, surfaces and spaces. The coordinates are the point’s ‘address’, its location relative to a known position called the origin, within a two- or three-dimensional grid on a flat surface or rectangular 3D space. In these situations, the exact, unique position of each data point or map reference is defined by a pair of (x,y) coordinates (or (x,y,z) in three dimensions). In most everyday applications, such as drawing a graph or reading a map, you would use the principles of Cartesian coordinate systems. Our page on Cartesian Coordinates introduces the simplest type of coordinate system, where the reference axes are orthogonal (at right angles) to each other. Understanding Statistical Distributions.Area, Surface Area and Volume Reference Sheet.Simple Transformations of 2-Dimensional Shapes.Polar, Cylindrical and Spherical Coordinates.Introduction to Cartesian Coordinate Systems.Introduction to Geometry: Points, Lines and Planes.Percentage Change | Increase and Decrease.Mental Arithmetic – Basic Mental Maths Hacks.Ordering Mathematical Operations - BODMAS.Common Mathematical Symbols and Terminology.