I'm having some problems with implementing the `express` function. This function would be called on a vector and would take a CoordSys object as and argument. The function should return a vector expressed in the CoordSys provided to this method.
Now, as a first step, we need to take care of the position. Say, we have two coordinate systems, C0 and C1, each having their origin at a different point in space. Now, we have a vector field in C1, say F. Now, we know the position coordinates of each of the frames in the global frame. But, these coordinates could have been expressed in any coordinate system. So, here's the algo: 1. Convert the position of both C0 and C1 into rectangular coordinates. 2. Subtract both the positions term wise. This way, we will have the difference of coordinates between C0 and C1. 3. Now, we can have relations such as: x0 = x1 + a y0 = y1 + b z0 = z1 + c -----------------Equations (*) Where the variables suffixed with 0 are in C0 and similarly for C1. 4. Now, we need to convert F from whatever coordinate system it was expressed in to rectangular so that we can substitute the variables from system (*). Also, we need to convert the base vectors to rectangular coordinates - because they stay constant throughout space. 5. Now, we have F in C1 expressed in rectangular coordinates. Now, substitute from system (*) into F. Base vectors remain the same because F has already been converted to rectangular coordinates. 6. Now effectively, we have F in C0, albeit in rectagular coordinates. Now, we can proceed from here to take care of orientation or change the coordinates back to some other coordinate system (spherical for example). Now, I want you guys to verify whether the procedure I have written above is correct or not. ----------------------- Now, we have to take care of the orientation. Now that we have positioned ourselves at C0, let as say we need to rotate C0 to another coordinate system, Cr, where C0 and Cr have the same origin. We already have the DCM between C0 and Cr. Now, I need to ask something. Does DCM represent the relation between coordinate variables or does it represent relation between coordinate variables? Or does it represent the relation between base vectors? Or both? Because of the way the DCM is derived, I think that it is the relation should hold for both. Is that correct? -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at http://groups.google.com/group/sympy. For more options, visit https://groups.google.com/groups/opt_out.
