Using Right-Handed Coordinates: Exploring Solutions

[ChiralSuperfields]

Homework Statement

Why did they not use a right-handed coordinate system for the part (a) of the problem below?

Relevant Equations

L = r cross p, where L, r, and p are vectors

Hi!

For this problem,

Why did the solutions choose to use a different coordinate system? I choose to use the right-handed coordinate system.

Many thanks!

 

[Filip Larsen]

Why did the solutions choose to use a different coordinate system?

Are you saying you don't consider East, North and Up to form a right-hand system? If so, you may want to reconsider.

 

[ChiralSuperfields]

Thanks for your reply! Is the coordinate system they used the most commonly used for the earth?

Many thanks!

 

[ChiralSuperfields]

Are you saying you don't consider East, North and Up to form a right-hand system? If so, you may want to reconsider.

Thanks for your reply, I have not really done left-handed coordinate systems yet. I have only right-handed coordinate systems so I'm not really too sure how to compare it too.

 

[haruspex]

Homework Statement:: Why did they not use a right-handed coordinate system for the part (a) of the problem below?
Relevant Equations:: L = r cross p, where L, r, and p are vectors

Hi!

For this problem,
View attachment 317935
Why did the solutions choose to use a different coordinate system? I choose to use the right-handed coordinate system.
View attachment 317937
Many thanks!

If East is positive x, North is positive y and up is positive z then (x,y,z) is right handed. (y,z,x), (z,x,y) would also be right handed. (z,y,x) would be right handed if you were to flip one direction, e.g. make West positive x, etc.

 

[nasu]

The answer is that the angular momentum is oriented in the southward direction. This won't change if you use a different coordinate system. There is no such thing as a coordinate system "most commonly used for Earth". The coordinate system used in the solution is right-handed. The direction of the unit vector $\hat{z}$ is obtained from $\hat{x}$ and $\hat{y}$ by the right-hand rule. ($\hat{z}$=$\hat{x} \times \hat{y}$)

 

[haruspex]

Are you saying you don't consider East, North and Up to form a right-hand system? If so, you may want to reconsider.

That doesn’t quite fix it. Those assignments can form a left- or right-handed system, depending on the order in which you write them in (,,). See post #5.

 

[Filip Larsen]

That doesn’t quite fix it. Those assignments can form a left- or right-handed system, depending on the order in which you write them

The order of the directions was, believe it or not, implied by the order it was written. If someone giving you directions say you need to turn left, right, and left, and you then turn right, left, and left because you didn't realize the order was important then you probably shouldn't be walking around alone in the first place.

So, yes, I was assuming the OP was aware that order of the axes are important for determining whether a list of axes form a right-hand system and therefore I didn't mention it. If nothing else, I assume he is aware now if he weren't before, just as I assume you can pick up that I think you are nitpicking :)

 

[ChiralSuperfields]

Thank you haruspex, nasu and Filip Larsen! I think I understand now.