How to multiple two rotation matrixes togheter

[sudden garden]

Depending on what you’re doing, you should be able to just add the angles in a new rotation matrix

[fierce parcel]

im rotating a cube first 45 degrees around the z axis and then 45 degrees around the x axsis but i wanna combine theese two rotation matrixes to skip extra steps.

[sudden garden]

Oh then it’s slightly different

What are your two matrices, since you already said the angles are fixed

Then you can deal with the matrix as usual, with explicit values in case you’re not already doing that

[fierce parcel]

its just the x matrix and z matrix when i combine them i get this

cos 45 , 0 , 0
0 ,cos(45) * cos(45) , 0
0 , 0 , cos(45)

[sudden garden]

How exactly are you combining them?

[fierce parcel]

i just mutliple them togheter

[sudden garden]

I mean show your work

Since apparently you’re not doing it right if I understand you correctly?

[fierce parcel]

i did it on a piece of paper but its really hard to understand since i did most of the work in my head

i dont think im doing it right either, its just something i came up with on the spot

[sudden garden]

So what do you want help with?

[fierce parcel]

i wanna know how to combine two matrixes togheter

[sudden garden]

So give me your two matrices and I’ll show you

Also the order in which you do it matters

You want to multiple them in the order (x matrix) ( z matrix ), do you see why?

[fierce parcel]

its just the rotation matrix for Z and Y

i mean Z and X

and i wanna start with Z first

[sudden garden]

When multiplying matrices, you dot the row and columns, and the index of of each row and colum corresponds to which element

So for the first element of our product

We will dot (1,0,0) (the first row of the x matrix)

And (cos theta, sin theta, 0) (the first column of the z matrix)

What number do you get when you dot these?

When I say dot I mean dot product btw

[fierce parcel]

ahaaaa, its just how you caculate a regulat matrix, we did learn about matrix multiplication but i was thinking outside of the problem that it didnt occur in my mind ahahha, thanks for clarifying it

[sudden garden]

Ur welcome!

Yeah after all these are matrices

So it shouldn’t be different

However, it could be different in the sense that it’s easier to combine depending on which type of rotations you’re doing