Originary curves

We call originary curve the curve for that at baseline the Frenet trihedron TNB coincides with the cartesian trihedron IJK. Therefore, the originary curve is the curve that passes through the origin of the cartesian landmark and for that at the origin the tangent vector to the curve coincides with the unit vector of axis OX , the normal vector coincides with the unit vector of axis OY, and the binormal vector coincides with the unit vector of axis OZ.

Originary curves have two remarkable properties: a mathematical property and a physical property .

-1) . The mathematical property is given by the fact that for the originary curve is sufficient to know its natural equation to be able to determine unambiguously the cartesian equation. This follows from the fundamental theorem of space curves, which says that two curves that have the same natural equation differ only by a translation and a rotation. Because two originary curves pass through the origin and have the same orientation, it follows that two originary curves that have the same natural equation will be identical, so they have the same cartesian equation .

-2) . The physical property is given by the fact that there are lots of experiments where the originary curves occur. For example, in the experiments in which a stream of particles enters into a room or get out from such room (piston, accelerator, detector, cloud chamber). Or interference experiments performed with light or with microparticles. Also, even the current Big Bang can be considered as a source of originary curves. So there are so many experiments in which originary curves occur, that they should be fully exploited as becometh.
 
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Is there a question here?
 
I believe so, but that it is implicit. It is, in fact, the following: it may be benefic this notion?
 
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I believe so, but that it is implicit. It is, in fact, the following: it may be benefic this notion?
Well, where did you first read about this notion? Didn't they provide some clue about how it's beneficial?
 
It is a notion about I think by myself, being troubled about the link between natural equation and cartesian equation. I believe that the study of natural equation lead to simplification of the laws of nature.
 
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Well, if it's something you found yourself, then that's original research. And that is forbidden on PF. Thread locked.
 

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