如何用实际向量创建一个可以在坐标系之间转换的向量函数？

Question

我看到了这个[答案][1] https://stackoverflow.com/questions/46993819/how-to-create-a-vector-function-in-sympy 它使用

Matrix()

作为解决方法。

我需要将输入和输出向量从一个坐标系转换到另一个坐标系（并返回）。在这种情况下向量函数是如何完成的？我的功能很简单：

def B_el(r_vec):
    r1 = r_vec.i
    r2 = r_vec.j
    u = sin(r1)+cos(r2)
    v = -cos(r1)+sin(r2)
    return Matrix([u, v, 0])

Answer 1

我建议您使用“向量”中描述的坐标系（下文中的 csys） https://docs.sympy.org/latest/modules/vector/coordsys.html

这是迄今为止我找到的最好的解决方案。

from sympy import symbols
from sympy.vector import CoordSys3D, express

grd = CoordSys3D('grd')
# this declares the existence of a csys, named grd

alpha, X, Y, Z = symbols('alpha, X, Y, Z')

slo = grd.orient_new_axis('slo', alpha, grd.k, location=2*grd.j)
# This creates a new csys named slo, rotated with an angle alpha around 
# the axis k of grd (=grd.k), and locates it at 2 on the axis j of grd
# (x y z are replaced by i j k)

V = X*slo.i + Y*slo.j + Z*slo.k
# this defines a vector V with coordinates (X, Y, Z), in the csys slo.

display(V)
display(express(V, slo))
display(express(V, grd))
# this will display the coordinates of the vector V, and then express its coordinates
# in the csys slo & grd.