Originary Curves: Mathematical & Physical Properties

  • Thread starter Abel Cavaşi
  • Start date
  • Tags
    Curves
In summary, originary curves are curves where the Frenet trihedron TNB at baseline coincides with the cartesian trihedron IJK. They have two remarkable properties: a mathematical property which allows for the determination of the cartesian equation from the natural equation, and a physical property where they occur in many experiments. The notion of originary curves was discovered through original research and is considered forbidden on PF.
  • #1
Abel Cavaşi
34
2
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.
 
Physics news on Phys.org
  • #2
Is there a question here?
 
  • #3
I believe so, but that it is implicit. It is, in fact, the following: it may be benefic this notion?
 
  • #4
Abel Cavaşi said:
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?
 
  • #5
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.
 
  • #6
Well, if it's something you found yourself, then that's original research. And that is forbidden on PF. Thread locked.
 

1. What are originary curves?

Originary curves are a mathematical concept used to describe curves that have a unique starting point, known as the origin. This origin is defined as the point where the curve begins to deviate from a straight line.

2. What are the physical properties of originary curves?

Originary curves have several physical properties, including their shape, length, and curvature. The shape of originary curves can vary, but they all have a distinct origin point. The length of an originary curve is defined as the distance from its origin to its end point. The curvature of an originary curve is determined by the rate at which it deviates from a straight line.

3. How are originary curves different from other types of curves?

Originary curves are unique in that they have a clearly defined starting point, unlike other curves which may have multiple or no starting points. Additionally, the curvature of an originary curve is always positive, whereas other curves can have both positive and negative curvature.

4. What are some real-world applications of originary curves?

Originary curves have various applications in fields such as physics, engineering, and computer graphics. They can be used to model the shape of objects in motion, such as a swinging pendulum or a rollercoaster track. In computer graphics, originary curves are used to create smooth and realistic animations.

5. How are originary curves related to calculus?

Originary curves are closely related to calculus, specifically differential calculus. The derivative of an originary curve at any point is equal to the slope of the tangent line at that point. This property is useful in calculating the curvature and other physical properties of originary curves.

Similar threads

Replies
4
Views
1K
Replies
72
Views
5K
  • Differential Geometry
Replies
9
Views
5K
  • Linear and Abstract Algebra
Replies
1
Views
863
  • Special and General Relativity
Replies
1
Views
618
Replies
14
Views
1K
  • Special and General Relativity
Replies
7
Views
1K
  • Special and General Relativity
Replies
1
Views
729
Replies
19
Views
1K
  • Special and General Relativity
2
Replies
51
Views
2K
Back
Top