def rotation_matrix(self, other):
"""
Returns the direction cosine matrix(DCM), also known as the
'rotation matrix' of this coordinate system with respect to
another system.
If v_a is a vector defined in system 'A' (in matrix format)
and v_b is the same vector defined in system 'B', then
v_a = A.rotation_matrix(B) * v_b.
A SymPy Matrix is returned.
Parameters
==========
other : CoordSysCartesian
The system which the DCM is generated to.
Examples
========
>>> from sympy.vector import CoordSysCartesian
>>> from sympy import symbols
>>> q1 = symbols('q1')
>>> N = CoordSysCartesian('N')
>>> A = N.orient_new_axis('A', q1, N.i)
>>> N.rotation_matrix(A)
Matrix([
[1, 0, 0],
[0, cos(q1), -sin(q1)],
[0, sin(q1), cos(q1)]])
"""
from sympy.vector.functions import _path
if not isinstance(other, CoordSysCartesian):
raise TypeError(str(other) +
" is not a CoordSysCartesian")
#Handle special cases
if other == self:
return eye(3)
elif other == self._parent:
return self._parent_rotation_matrix
elif other._parent == self:
return other._parent_rotation_matrix.T
#Else, use tree to calculate position
rootindex, path = _path(self, other)
result = eye(3)
i = -1
for i in range(rootindex):
result *= path[i]._parent_rotation_matrix
i += 2
while i < len(path):
result *= path[i]._parent_rotation_matrix.T
i += 1
return result
def position_wrt(self, other):
"""
Returns the position vector of this Point with respect to
another Point/CoordSysCartesian.
Parameters
==========
other : Point/CoordSysCartesian
If other is a Point, the position of this Point wrt it is
returned. If its an instance of CoordSyRect, the position
wrt its origin is returned.
Examples
========
>>> from sympy.vector import Point, CoordSysCartesian
>>> N = CoordSysCartesian('N')
>>> p1 = N.origin.locate_new('p1', 10 * N.i)
>>> N.origin.position_wrt(p1)
(-10)*N.i
"""
if (not isinstance(other, Point) and
not isinstance(other, CoordSysCartesian)):
raise TypeError(str(other) +
"is not a Point or CoordSysCartesian")
if isinstance(other, CoordSysCartesian):
other = other.origin
# Handle special cases
if other == self:
return Vector.zero
elif other == self._parent:
return self._pos
elif other._parent == self:
return -1 * other._pos
# Else, use point tree to calculate position
rootindex, path = _path(self, other)
result = Vector.zero
i = -1
for i in range(rootindex):
result += path[i]._pos
i += 2
while i < len(path):
result -= path[i]._pos
i += 1
return result