Spherical Vector Addition Process

[n00bcake22]

Hello Everyone,

I was just wondering if there was a way to add two vectors that are determined by spherical coordinates (radius, theta, phi). For example, if I have v1 = (5, Pi/4, Pi/2) and v2 = (3, Pi, -Pi/2) is there a way to add these using their respective radii, thetas, and phis or do I HAVE to convert them to Cartesian coordinates first, perform the addition, and then convert back?

Also, if anybody knows, what is the difference between "bound" and "free" vectors? I was looking around and this came up but the description was a bit fuzzy.

Thanks again!

 

[tiny-tim]

hello n00bcake22!

I was just wondering if there was a way to add two vectors that are determined by spherical coordinates (radius, theta, phi). For example, if I have v1 = (5, Pi/4, Pi/2) and v2 = (3, Pi, -Pi/2) is there a way to add these using their respective radii, thetas, and phis or do I HAVE to convert them to Cartesian coordinates first, perform the addition, and then convert back?

there's probably a way of doing it once you've found the angle between the two vectors

but converting to Cartesian is the only easy way

what is the difference between "bound" and "free" vectors?

a free vector is like velocity … you can slide it about anywhere, especially when you want to add it to another vector

a bound vector is like force … you can't slide it about unless you compensate by adding a couple … a bound vector is really a pair, the vector itself and the line of application

 

[n00bcake22]

Thanks tiny-tim!

Converting to Cartesian and back it is! :) Is this the suggested method for all vector operations (dot/cross product, etc.)?

Could you give a slightly more verbose example of “bound” and “free” vectors? I am still a bit confused.

Using your examples, a force A i^ + B j^ + C k^ (bound?) is acting on a point mass M whose velocity is D i^ + E j^ + F k^ (free vector?). I fail to see the difference. :(

 

[tiny-tim]

hi n00bcake22!

Converting to Cartesian and back it is! :) Is this the suggested method for all vector operations (dot/cross product, etc.)?

yes (except for very simple cases)

Could you give a slightly more verbose example of “bound” and “free” vectors? I am still a bit confused.

Using your examples, a force A i^ + B j^ + C k^ (bound?) is acting on a point mass M whose velocity is D i^ + E j^ + F k^ (free vector?). I fail to see the difference. :(

we don't usually want to add velocities …

although we often add the force on two different points, or the momentum of two different points, we never have any reason to add the velocities of two different points …

but we do add relative velocities, and when we add them the line through which they act doesn't matter, so velocity is a free vector