Orbital coordinates in motion
Of ferman: Fernando Mancebo Rodriguez--- Personal page. ----Spanish pages

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"Orbital coordinates are spherical coordinates in motion"

Easy definition: "" Given a central point of reference C, the orbital or radial coordinates define us, locate and measure any movement, distance and speed with respect to C of any of the "particles" P that are located or they move in the sphere around C.""

You can also deduce the future situation of these "particles" at a time t.
Geometrically also, the orbital or radial coordinates can draw us multiple types of geometric figures, such as rotation figures, spirals, springs, screws, polygons of all kinds, stars, cones, pyramids, spheres, cylinders, etc.

These coordinates do not use, as a basis, the trigonometry parameters of union with the Cartesian coordinates (sin, cos, etc.), but the angular velocity vectors W and the linear velocity vectors V, both together to a time vector that It is common And it makes the orbitals move.
Also these coordinates can be used without movement, stopping the time, to see the situation of the orbitals at any time.
In the same way, to predict where they can be found at a future time t.

This way, this coordinates type can be defined as dynamic geometry

The orbital coordinates are a system of spherical coordinates that are used as group when being united and developing all their parameters by means of a time vector.
This vector of time -taking it from its beginning until its finalisation- unites and makes work to the whole group of formulas and parameters, with which the result can express us motions and geometric figures.
For it, we apply the formulas of radial coordinates to an imaginary particle (P) that travels and draws us movements, drawings and geometric figures that we want to build.
In the drawing this system is shown; in which P is the imaginary particle that will describe us the figures that we would compose.
--C is the centre or support point from where we will build the figure or motion.
--R is the radius or distance from the centre C to the particle P in each moment.
--O or Alfa, is the radial coordinate in horizontal sense. This coordinate is measured in degrees and in angular speed (Wo)
--H or Beta, is the vertical coordinate that is measured from the horizontal coordinate O. It is measured in degrees and angular speed Wh.
--t is the time that unites to all the parameters of each formula and impels them motion.
Besides these simplified formulas, in many cases we can substitute parameter of angular speed (W.t) for vectors of speed (v.t).
For example, the angular speed of H, (Wh) can be substituted by a displacement vector (v.t) of the point C toward the vertical H.
Addition of more coordinates and vectors of motion can be made in formulas also.

Many are the geometric figures that can be built with these orbital coordines.As example I put the construction of spirals and other geometric figures.

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Orbitals ones.

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Clock

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Spherical expansion, bubble or big-bang / and springs

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Sphere

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Pendulum

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