How to calculate coordinates

How to calculate coordinates

There are three main systems of the coordinates used in geometry, theoretical mechanics, other sections of physics: Cartesian, polar and spherical. In these systems of coordinates each point has three coordinates which completely set the provision of this point in three-dimensional space.

It is required to you

Cartesian, polar and spherical systems of coordinates

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Instruction

1

Consider for a start rectangular Cartesian system of coordinates. The position of a point in space in this system of coordinates is defined by coordinates x, y and z. From the beginning of coordinates to a point radius vector is carried out. Projections of it radius vector on coordinate axes will also be coordinates of this point. Radius vector of a point can also be presented as a diagonal of a rectangular parallelepiped. Point projections to coordinate axes will coincide with tops of this parallelepiped.

2

Consider now polar system of coordinates in which the coordinate of a point will be set by the radial coordinate of r (radius vector in the XY plane), angular coordinate? (a corner between a vector of r and axis X) and the coordinate of z similar to z coordinate in the Cartesian system.
Polar coordinates of a point can be translated in Cartesian as follows: x = r*cos?, y = r*sin?, z = z.

3

Now consider spherical system of coordinates. In it the provision of a point is set by three coordinates of r? and?. r - distance from the beginning of coordinates to a point? and? - azimuthal and antiaircraft corner respectively. Corner? it is similar to a corner with the same designation in polar system of coordinates, and? - the corner between radius vector r and axis Z, and 0 If to translate spherical coordinates in Cartesian, will turn out: x = r*sin? *cos?, y = r*sin? *sin? *sin?, z = r*cos?.