Calculate velocity components x,y and z

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Discussion Overview

The discussion revolves around calculating the velocity components (x, y, and z) in a three-dimensional environment based on a given velocity value and two angles (yaw and pitch). The scope includes theoretical understanding and practical application, particularly in programming a simulation for projectile motion.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant seeks to calculate the x, y, and z components of velocity using yaw and pitch angles, expressing familiarity with 2D calculations but uncertainty in 3D.
  • Another participant questions the reference axis for pitch, suggesting that it may relate to the x-axis and noting the potential confusion with angle definitions.
  • A later reply proposes that if the yaw is relative to the z-axis, the pitch should be clarified in terms of its relationship to the x or y-axis, emphasizing the need for clear definitions of the axes involved.
  • One participant expresses a desire to avoid using spherical coordinates, suggesting a preference for translating initial conditions into velocity components directly.
  • Another participant acknowledges the complexity of spherical coordinates and expresses a willingness to learn more about them.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the definitions and relationships of the angles involved, indicating multiple competing views on how to approach the problem of calculating velocity components in 3D.

Contextual Notes

There are unresolved questions regarding the definitions of yaw and pitch, as well as their reference axes, which may affect the calculations. The discussion also highlights the potential confusion arising from different conventions in representing angles.

Redweasel
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Hello,

I want to calculate the velocity components x, y and z based on a velocity value and two angles (yaw along the z-axis and pitch).

I know how to calculate the x and y components in an 2D-environment:
initial velocity x = initial velocity * cos(theta)
initial velocity y = initial velocity * sin(theta)

But I can't figure out to apply this to an 3D-environment. Can anybody give me some good resources for learning this concept or provide some examples?

Many thanks in advance!

Redweasel
P.S.: Sorry for my bad english
 
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Redweasel said:
I want to calculate the velocity components x, y and z based on a velocity value and two angles (yaw along the z-axis and pitch).
If the yaw is relative to z axis, then which axis is pitch relative to? This sound similar to spherical coordinates, with r equal to the magnitude of velocity. Note that there are conflicting usages of the symbols used to represent the angles. Link to mathworld article:

http://mathworld.wolfram.com/SphericalCoordinates.html
 
The pitch should be related to the x axis.

The purpose for this is java programming. I want to create a little program where you enter the initial velocity, yaw and pitch and then throw a ball. It then displays the time when it hits the floor (time = zInitialVelocity / g * 2) and the x and y coordinates. Is there a way without the spherical coordinate system?
 
Redweasel said:
The pitch should be related to the x axis.
Related to the x-axis in which direction, towards the y-axis or towards the z axis? You didn's specify the relationship bettween x, y, z axis and the directions left-right, forward-back, up-down. If z-axis is vertical, then pitch could be the angle from horizontal (the x-y plane) (which could be restated as π/2 - angle from z-axis), and yaw would be the angle from x or y-axis along the x-y plane.

Redweasel said:
I want to create a little program where you enter the initial velocity, yaw and pitch and then throw a ball. It then displays the time when it hits the floor (time = zInitialVelocity / g * 2) and the x and y coordinates. Is there a way without the spherical coordinate system?
A velocity, yaw, and pitch implies a spherical like coordinate (magnitude and two angles). You can always translate the initial condition into components of velocity vx, vy, vz. Acceleration can also be split up into ax, ay, az components and position would be x, y, z.
 
Last edited:
I guess I have to learn this spherical coordinate stuff then. Looks quite confusing, but I think I'll find a way. Thanks for your answer
 

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