Converting Frenet TNB Coordinates to Cylindrical Coordinates

In summary, the conversation is about converting a circular helix, defined using the Frenet tnb triad, to a cylindrical coordinate system RTZ. The tangent of the helix t is oriented at angle A with respect to the base of the cylinder and the conversion formula is R = -n, T = t cos(A) - b sin(A), Z = T sin(A) + b cos(A). The person is seeking clarification on whether this conversion is correct.
  • #1
caejournal
2
0
Hi all,

I have a circular helix with any point on the helix defined using the Frenet tnb triad.
t- tangent, b- binormal and n-normal acting towards the axis of the host circular cylinder.

The tangent of the helix t is oriented at angle A with respect to the base of the cylinder.

Now I want to convert the tnb coord system to the cylindrical coordinate system, RTZ. I need it because the cylinder has to be defined in terms of RTZ.

I came up with this:
R = -n
T = t cos(A) - b sin(A)
Z = T sin(A) + b cos(A)

Is this correct? (T is implicit in RTZ for representing a helix in cylindrical CSYS). I am confused. Any help would be appreciated. Thanks

-C
 
Physics news on Phys.org
  • #2
Anyone? Please...
 

1. What are cylindrical coordinates?

Cylindrical coordinates are a type of coordinate system in three-dimensional space that uses a combination of a radial distance, an azimuthal angle, and a height or vertical position to locate points. It is often used to describe the position and movement of objects in cylindrical or circular shapes.

2. What is a helix in cylindrical coordinates?

A helix in cylindrical coordinates is a three-dimensional curve that is formed by a constant angle of rotation and a constant change in height or vertical position as it moves along a circular path. It can be described using the cylindrical coordinates of the points along its path.

3. How is a helix different from a spiral?

A helix and a spiral are often used interchangeably, but there are some key differences. A helix is a three-dimensional curve, while a spiral is a two-dimensional curve. Additionally, a helix has a constant angle of rotation and a constant change in height, while a spiral may have varying angles and distances between each turn.

4. What are the applications of helix in cylindrical coordinates?

Helices in cylindrical coordinates have various applications in science and engineering. They can be used to describe the structure of DNA, the shape of protein molecules, and the movement of objects such as screws and bolts. They are also used in mathematical models for fluid dynamics, electromagnetics, and other physical phenomena.

5. How do you convert between cartesian and cylindrical coordinates for a helix?

To convert between cartesian and cylindrical coordinates for a helix, you can use the following equations:

x = r*cos(theta)

y = r*sin(theta)

z = h

where r is the radial distance, theta is the azimuthal angle, and h is the height or vertical position. These equations can also be used in reverse to convert from cylindrical coordinates to cartesian coordinates.

Similar threads

I Connection forms and dual 1-forms for cylindrical coordinate
    • Differential Geometry
Replies
3
Views
2K
B Helix in intrinsic coordinates?
    • Classical Physics
Replies
6
Views
760
I Coordinate systems vs. Euclidean space
    • Differential Geometry
Replies
9
Views
3K
I Convert cylindrical coordinates to Cartesian
    • Linear and Abstract Algebra
Replies
6
Views
923
I Tangent space basis vectors under a coordinate change
    • Differential Geometry
Replies
12
Views
3K
Eigenvalues of the Frenet formulas and angular velocity
    • Differential Geometry
Replies
1
Views
2K
The TNB components of the jerk vector
    • Other Physics Topics
Replies
1
Views
2K
Kinematics in Cylindrical Coordinates
    • Calculus and Beyond Homework Help
Replies
4
Views
2K
I Einstein Definition of Simultaneity for Langevin Observers
    • Special and General Relativity
Replies
12
Views
1K
Good coordinates and degrees of freedom
    • Introductory Physics Homework Help
Replies
2
Views
3K

Hot Threads

Recent Insights

Back
Top