Easy addition of polar vectors?

[byoung]

I'm trying to add polar vectors, which is easily accomplished on the 50g or 48 series using cylindrical or spherical mode. Specifically, I'm learning the Prime by duplicating example 3 on page 178 of the HP48SX manual. In this example, we want to add three vectors (I'll use "<" to represent the angle symbol):

[170 <143] + [185 <62] + [100 <-99] = [178.937 <111.149]

This resultant is then resolved along the 175 degree line by taking the dot product with [1 <175] to get 78.86.

I can achieve the first part using a ridiculous number of conversions with the rectangular_coordinates() and polar_coordinates() commands. The last part is even worse because I have to convert the resultant and the [1 <175] vector back to rectangular coordinates and the copy and paste both of these into the dot() command.

This seems much more complicated than it should be to do a routine, basic engineering calculation. Am I missing something obvious? Also, I can only do this in CAS. I'd prefer RPN, but this seems out of the question.

Thanks.

[Joe Horn]

There might be an easier way, but this is pretty simple:
   

[Wes Loewer]

(10-28-2023 09:34 PM)byoung Wrote:  I'm trying to add polar vectors, which is easily accomplished on the 50g or 48 series using cylindrical or spherical mode. Specifically, I'm learning the Prime by duplicating example 3 on page 178 of the HP48SX manual.

For my own use, this lack of ability to display vectors in cylindrical or spherical modes is one of the more glaring mathematical omissions of the Prime. The Prime is my "go to" calculator when I'm teaching calculus and precalculus, but in my physics classes, I usually reach for my 50g mainly for this reason.

When I was a beta tester for the Prime, I brought this up on more than one occasion. As I recall, at one point Tim said that this feature was not possible. However, on a later occasion he suggested that it might be easier than he first thought. In any case, priorities being what they are, this feature was never added. It's too bad as it seemed to me to be a step back from the 48/49/50.

Some years back one of my physics students asked me, "Did you just convert that vector with a single button?" After class I showed him how I had set up a custom "physics" menu which included a soft button to toggle rectangular/spherical mode. He went right out and bought a 50g for himself. I can say with confidence that this feature sold at least one calculator.

[Wes Loewer]

(10-29-2023 12:28 AM)Joe Horn Wrote:  There might be an easier way, but this is pretty simple:

In case anyone is wondering, the clever technique that Joe is illustrating works because Home can display complex numbers in polar form while CAS.dot and CAS.cross products will treat complex as 2d vectors. (CAS.cross returns the z component.)

This won't work with 3d vectors.

[byoung]

(10-29-2023 12:28 AM)Joe Horn Wrote:  There might be an easier way, but this is pretty simple:

Thanks Joe, that's pretty easy. I didn't think of this because it seems odd to me that the CAS function dot() would have to be used outside of CAS for this to work. In any case, it's much better than my method!

[byoung]

(10-29-2023 04:07 AM)Wes Loewer Wrote:  

(10-28-2023 09:34 PM)byoung Wrote:  I'm trying to add polar vectors, which is easily accomplished on the 50g or 48 series using cylindrical or spherical mode. Specifically, I'm learning the Prime by duplicating example 3 on page 178 of the HP48SX manual.

For my own use, this lack of ability to display vectors in cylindrical or spherical modes is one of the more glaring mathematical omissions of the Prime. The Prime is my "go to" calculator when I'm teaching calculus and precalculus, but in my physics classes, I usually reach for my 50g mainly for this reason.

When I was a beta tester for the Prime, I brought this up on more than one occasion. As I recall, at one point Tim said that this feature was not possible. However, on a later occasion he suggested that it might be easier than he first thought. In any case, priorities being what they are, this feature was never added. It's too bad as it seemed to me to be a step back from the 48/49/50.

Some years back one of my physics students asked me, "Did you just convert that vector with a single button?" After class I showed him how I had set up a custom "physics" menu which included a soft button to toggle rectangular/spherical mode. He went right out and bought a 50g for himself. I can say with confidence that this feature sold at least one calculator.

Agreed. I bought the Prime as a replacement for my aging 50g, but I don't think it will ever be my go-to machine. The Prime is better than previous HPs at some things, and definitely faster, but I find myself spending more time figuring out how it wants me to do things than actually getting work done. Also, I was a bit disappointed by your comment that Joe's method won't work on 3D vectors, but who needs those crazy things anyway?

Thanks for the input.