When Gilbert used the base scalars in the vector expression, the equation was just the mathematical way to convert the base scalars from one frame to another. It wasnt a position vector per say. The point was, that the relations that you would get between the variables on the lhs and rhs are the relationships the base scalars should show wrt each other. About going via a global frame, though its the multiplication of only two matrices in your cases, calculating the matrices themselves is a tough task. For eg, in the current framework, try defining 100 frames each wrt the former, and then find the dcm of the 98th wrt the 96th using the current, 'tree way'..I tried doing it your way, it just gets stuck. The issue is the time complexity in calculation and simplification. As it is, when you store the dcm of the 100th frame wrt the first, you will need to multiply its dcm wrt 99th with the dcm of the 99th wrt Global, and this follows a recursive definition, which mathematically means multiplying 99 dcms. On Jul 10, 2013 9:51 PM, "Prasoon Shukla" <prasoon92.i...@gmail.com> wrote:
> @Stefan : For the case you mention, there's another step that converts > between coordinate systems. For the case of U and V (as you mentioned), > we'll just convert from U to V. Here are the steps: > > 1. We substitute for x, y, z (base scalars of U) in terms of rho, phi, z > (base scalars of V). Then, there's a conversion matrix between coordinate > systems - we apply that transformation to the vector that we got after > transformation. This gives us the vector in V. > > Anyway, it was getting very difficult for me to read the obscure notation > that we are using here on this thread. So, I think that the points will be > clearer in latex. > > My reply to you guys has therefore been posted here : http://mathb.in/8583 > > This sheet is editable and is latex enabled. > > On Wednesday, July 10, 2013 4:35:10 PM UTC+5:30, Stefan Krastanov wrote: >> >> @Prasoon, maybe I misunderstood what you suggest, but on first glance it >> seems it will work awfully in the following case: >> >> coordinate systems: >> >> A (carthesian) -> B -> many more -> U -> V >> >> where U and V have the same origin and orientation but U is carthesian >> while V is polar. >> >> How will something defined in U will be expressed in V according to your >> suggestion? >> > -- > You received this message because you are subscribed to a topic in the > Google Groups "sympy" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/sympy/t-Je0beTIIU/unsubscribe. > To unsubscribe from this group and all its topics, 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. > > > -- 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.
