- #1
MannyZanny
- 3
- 0
I am working on developing a physics engine and I'm having trouble isolating a vector variable from an equation. The entire equation is quite lengthy but I know how to figure out the rest if I find a way to move some variables around. I am much stronger in developing equations in calculus but not so much in linear algebra. Here is a small snippet:
j/m + ((r x j) x r)/I
j/m is vector j divided by scalar m, x is a cross product and I is a 3x3 matrix that is diagonal, sorry not sure of the proper term.
ie. I =
[x 0 0]
[0 x 0]
[0 0 x]
I am trying to factor out j to get something like j ( 1/m + (r x r)/I) so I can move that part to the other side of the equation ending in j=... I realize it's not a full equation which may make it more difficult for you to help me. I have worked out a simpler version of this equation but I can't figure this one out and I've spent hours trying to use identities and trying other things. I have read a couple papers that show these equations but one is expecting to solve component wise (jx = ... jy = ... jz = ...) which I know how to do but I wanted to get the matrix and vector solution. Another one shows the matrix solution but not how to arrive at that answer and uses some math notation I'm not sure of. Thanks for any help and if it is too hard without seeing the complete equation or you would like to see the papers I mentioned, let me know. I'll check the forum in the morning once I get some sleep :)
j/m + ((r x j) x r)/I
j/m is vector j divided by scalar m, x is a cross product and I is a 3x3 matrix that is diagonal, sorry not sure of the proper term.
ie. I =
[x 0 0]
[0 x 0]
[0 0 x]
I am trying to factor out j to get something like j ( 1/m + (r x r)/I) so I can move that part to the other side of the equation ending in j=... I realize it's not a full equation which may make it more difficult for you to help me. I have worked out a simpler version of this equation but I can't figure this one out and I've spent hours trying to use identities and trying other things. I have read a couple papers that show these equations but one is expecting to solve component wise (jx = ... jy = ... jz = ...) which I know how to do but I wanted to get the matrix and vector solution. Another one shows the matrix solution but not how to arrive at that answer and uses some math notation I'm not sure of. Thanks for any help and if it is too hard without seeing the complete equation or you would like to see the papers I mentioned, let me know. I'll check the forum in the morning once I get some sleep :)