- #1
kexanie
- 11
- 0
I've learned that a vector in coordinate system can be expressed as follows:
A = axAx+ayAy+azAz.
ai, i = x, y, z, are the base vectors.
The transformation matrix from cylindrical coordinates to cartesian coordiantes is:
Ax cosΦ -sinΦ 0 Ar
Ay = sinΦ cosΦ 0 mutiplye by AΦ
Az 0 0 1 Az
and the conversion formula
x = rcosΦ
y = rsinΦ
z = z
A = axAx+ayAy+azAz.
ai, i = x, y, z, are the base vectors.
The transformation matrix from cylindrical coordinates to cartesian coordiantes is:
Ax cosΦ -sinΦ 0 Ar
Ay = sinΦ cosΦ 0 mutiplye by AΦ
Az 0 0 1 Az
and the conversion formula
x = rcosΦ
y = rsinΦ
z = z
- What's the difference between this two kind of equations?
- Why Ax is not equal to x?
- I was told that Ax might be a function of x, y and z. Is the latter kind of equaltions has a prerequisite that ax = (1, 0, 0), but in the first kind of equations, the base vector can be anything else?
- From the matrix, Ax = cosΦAr - sinΦAΦ, that is not equal to x = rcosΦ !? Why? How should I apply the transformation matrix?