欧拉角
Extrinsic Rotation
内部旋转：
from sympy import symbols, cos, sin, pi, sqrt
from sympy.matrices import Matrix
### Create symbols for joint variables
q1, q2 = symbols('q1:3')
# Create a symbolic matrix representing an intrinsic sequence of rotations
# about the Y and then Z axes. Let the rotation about the Y axis be described
# by q1 and the rotation about Z by q2.
####### TO DO ########
# Replace R_y and R_z with the APPropriate (symbolic) elementary rotation matrices
# and then compute YZ_intrinsic.
R_y = Matrix([[ cos(q1), 0, sin(q1)],
[ 0, 1, 0],
[-sin(q1), 0, cos(q1)]])
R_z = Matrix([[ cos(q2), -sin(q2), 0],
[ sin(q2), cos(q2), 0],
[ 0, 0, 1]])
YZ_intrinsic_sym = R_y * R_z
####### TO DO ########
# Numerically evaluate YZ_intrinsic assuming:
# q1 = 45 degrees and q2 = 60 degrees.
# NOTE: Trigonometric functions in Python assume the input is in radians!
YZ_intrinsic_num = YZ_intrinsic_sym.evalf(subs={q1: pi/4, q2: pi/3})
外部旋转：
from sympy import symbols, cos, sin, pi, sqrt
from sympy.matrices import Matrix
### Create symbols for joint variables
q1, q2 = symbols('q1:3')
# Create a symbolic matrix representing an extrinsic sequence of rotations
# about the Z and then Y axes. Let the rotation about the Y axis be described
# by q1 and the rotation about Z by q2.
####### TO DO ########
# Replace R_y and R_z with the appropriate (symbolic) elementary rotation matrices
# and then compute ZY_extrinsic.
R_y = Matrix([[ cos(q1), 0, sin(q1)],
[ 0, 1, 0],
[-sin(q1), 0, cos(q1)]])
R_z = Matrix([[ cos(q2), -sin(q2), 0],
[ sin(q2), cos(q2), 0],
[ 0, 0, 1]])
ZY_extrinsic_sym = R_y * R_z
ZY_extrinsic_num = ZY_extrinsic_sym.evalf(subs={q1: pi/4, q2: pi/3})
####### TO DO ########
# Numerically evaluate ZY_extrinsic assuming:
# q1 = 45 degrees and q2 = 60 degrees.
# NOTE: Trigonometric functions in Python assume the input is in radians!
#ZY_extrinsic_sym =
#ZY_extrinsic_num = ZY_extrinsic_sym.evalf(subs{})
相关阅读
欧拉角（Euler Angles）用来描述坐标轴的旋转。 坐标轴原始坐标轴记为x−y−zx-y-zx−y−z，旋转后坐标轴记为X−Y−ZX-Y-ZX−Y−Z，坐标