I am putting together the components of a vector field (a magnetic field,
caused by a current in several conductors) in cartesian coordinates. The
field is derived from calculating the rotation of its magnetic vector
potential, which can be expressed as
A_z = -Const * dot(r,a)(dot(r,r)
A =(0,0,A_z
and then the rot(A):
B = curl(A)
gives me (after some simplifications)
u = (2 * C * r2 * (a1 * r1 + a2 * r2)) / np.square(r1*r1 + r2*r2) - (C *
a2) / (r1*r1 + r2*r2)
v = (C * a1) / (r1*r1 + r2*r2) - (2 * C * r1 * (a1 * r1 + a2 * r2)) /
np.square(r1*r1 + r2*r2)
w = 0
with B(u,v,w) being the vector field I am interested in.
My initial question ("How to create a vector") is mostly a sympy
syntactical one. I look for a function like
Sys = CoordSys3D("Sys")
O = Sys.origin
u = (2 * C * r2 * (a1 * r1 + a2 * r2)) / np.square(r1*r1 + r2*r2) - (C *
a2) / (r1*r1 + r2*r2)
v = (C * a1) / (r1*r1 + r2*r2) - (2 * C * r1 * (a1 * r1 + a2 * r2)) /
np.square(r1*r1 + r2*r2)
w = 0
V = O.vector(u,v,w)
^^^^^^^^^^^^^^^^^^^
where I can specify a vector, relative to a coordinate system, by its
components. The O.vector() function would return a vector that can then
safely be transformed into other (resting) coordinate systems.
brombo schrieb am Freitag, 22. Oktober 2021 um 19:06:03 UTC+2:
> You might want to look at this link -
>
> https://galgebra.readthedocs.io/en/latest/
>
> Also if you could show me symbolically (not code) what you are doing
> perhaps I could give you an example of how to do it in galgebra.
> On 10/22/21 3:15 AM, Andreas Schuldei wrote:
>
> I saw this
> https://stackoverflow.com/questions/46993819/how-to-create-a-vector-function-in-sympy
>
> which uses Matrix() as a workaround to create a vector. The author says,
> that it can not be transformed between coordinate systems, like real
> vectors, though.
>
> I need to transform my input and output vector from one coordinate system
> to another (and back). How are vector functions done in that case? My
> function is simple:
>
> def B_el(r_vec, I):
> mu_0 = 4 * np.pi * 1e-7
> a1 = -0.05
> a2 = 0.0
> C = mu_0 * I / np.pi
> r1 = r_vec.i
> r2 = r_vec.j
> u = (2 * C * r2 * (a1 * r1 + a2 * r2)) / np.square(r1*r1 + r2*r2) - (C *
> a2) / (r1*r1 + r2*r2)
> v = (C * a1) / (r1*r1 + r2*r2) - (2 * C * r1 * (a1 * r1 + a2 * r2)) /
> np.square(r1*r1 + r2*r2)
> return Matrix([u, v, 0])
>
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