Mathematics
Radial Coordinates
-Spanish
"The radial coordinates are a new system of coordinates (as group), which by means of using formulas that contain these coordinates you can create, move and transform bodies and geometric figures through the space during a certain period of time or indefinitely if we want."
With the radial coordinates you could build all type of figures and space bodies, and what is more important, we can apply them movement and we can go transforming them to our desires.
In this Web single basic formulas to be able to understand their content are detailed, but their reach and development capacity is limitless.
The system of radial coordinates is formed by spherical coordinates, several moving vectors and a period of time in which different mathematics functions are applied and developed on these coordinates.
So, radial coordinates consist on two angular coordinates (O and H) and for a distancing vector or radius (R) that goes from a central point (C) that is taken as reference point to an orbital one or particle (P) that rotates around this centre. The movement or displacement vectors are applied to each coordinate of the previous ones, and sometime to the whole group of coordinates.
Radial coordinates also use a time parameter or period of time (t) through which all its functions are developed. So that, we can cosider to radial coordinates as moving or living mathematics.
The formula is shown in the drawing and its parameters are the following ones:
Ps = Position of the particle on the sphere in any moment.
R = Radius or distance between the reference point (centre) and the particle or orbital.
O = Primary coordinate (horizontal) on which the secondary coordinate H is measured.
H = Secondary coordinate that indicates us the vertical angle that the particle have in any moment.
Oa = Angle that the O coordinate marks in each moment regard to the position of the particle.
Ha = Angle that the H coordinate has (It taken on the situation of the O coordinate)
wo = Angular speed (degrees for unit of time) that the O coordinate follows.
wH = Angular speed (g.u.t.) that the H coordinate follows.
V = Speed of distancing of the particle with regard to the centre C.
T = Time
As we can see in the drawing, the formula is represented with base R that represents the vector or distancing of the orbital one (particle) and for an index and a sub-index that show us the value of the radial coordinates.