<P> Spherical coordinates are useful in analyzing systems that have some degree of symmetry about a point, such as volume integrals inside a sphere, the potential energy field surrounding a concentrated mass or charge, or global weather simulation in a planet's atmosphere . A sphere that has the Cartesian equation x + y + z = c has the simple equation r = c in spherical coordinates . </P> <P> Two important partial differential equations that arise in many physical problems, Laplace's equation and the Helmholtz equation, allow a separation of variables in spherical coordinates . The angular portions of the solutions to such equations take the form of spherical harmonics . </P> <P> Another application is ergonomic design, where r is the arm length of a stationary person and the angles describe the direction of the arm as it reaches out . </P> <P> Three dimensional modeling of loudspeaker output patterns can be used to predict their performance . A number of polar plots are required, taken at a wide selection of frequencies, as the pattern changes greatly with frequency . Polar plots help to show that many loudspeakers tend toward omnidirectionality at lower frequencies . </P>

The earth's spherical coordinate system is an angular coordinate system