Orienter classes (docstrings)¶
Orienter¶
AxisOrienter¶
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class
sympy.vector.orienters.
AxisOrienter
(angle, axis)[source]¶ Class to denote an axis orienter.
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__init__
(angle, axis)[source]¶ Axis rotation is a rotation about an arbitrary axis by some angle. The angle is supplied as a SymPy expr scalar, and the axis is supplied as a Vector.
- Parameters
angle : Expr
The angle by which the new system is to be rotated
axis : Vector
The axis around which the rotation has to be performed
Examples
>>> from sympy.vector import CoordSys3D >>> from sympy import symbols >>> q1 = symbols('q1') >>> N = CoordSys3D('N') >>> from sympy.vector import AxisOrienter >>> orienter = AxisOrienter(q1, N.i + 2 * N.j) >>> B = N.orient_new('B', (orienter, ))
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BodyOrienter¶
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class
sympy.vector.orienters.
BodyOrienter
(angle1, angle2, angle3, rot_order)[source]¶ Class to denote a body-orienter.
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__init__
(angle1, angle2, angle3, rot_order)[source]¶ Body orientation takes this coordinate system through three successive simple rotations.
Body fixed rotations include both Euler Angles and Tait-Bryan Angles, see https://en.wikipedia.org/wiki/Euler_angles.
- Parameters
angle1, angle2, angle3 : Expr
Three successive angles to rotate the coordinate system by
rotation_order : string
String defining the order of axes for rotation
Examples
>>> from sympy.vector import CoordSys3D, BodyOrienter >>> from sympy import symbols >>> q1, q2, q3 = symbols('q1 q2 q3') >>> N = CoordSys3D('N')
A ‘Body’ fixed rotation is described by three angles and three body-fixed rotation axes. To orient a coordinate system D with respect to N, each sequential rotation is always about the orthogonal unit vectors fixed to D. For example, a ‘123’ rotation will specify rotations about N.i, then D.j, then D.k. (Initially, D.i is same as N.i) Therefore,
>>> body_orienter = BodyOrienter(q1, q2, q3, '123') >>> D = N.orient_new('D', (body_orienter, ))
is same as
>>> from sympy.vector import AxisOrienter >>> axis_orienter1 = AxisOrienter(q1, N.i) >>> D = N.orient_new('D', (axis_orienter1, )) >>> axis_orienter2 = AxisOrienter(q2, D.j) >>> D = D.orient_new('D', (axis_orienter2, )) >>> axis_orienter3 = AxisOrienter(q3, D.k) >>> D = D.orient_new('D', (axis_orienter3, ))
Acceptable rotation orders are of length 3, expressed in XYZ or 123, and cannot have a rotation about about an axis twice in a row.
>>> body_orienter1 = BodyOrienter(q1, q2, q3, '123') >>> body_orienter2 = BodyOrienter(q1, q2, 0, 'ZXZ') >>> body_orienter3 = BodyOrienter(0, 0, 0, 'XYX')
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SpaceOrienter¶
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class
sympy.vector.orienters.
SpaceOrienter
(angle1, angle2, angle3, rot_order)[source]¶ Class to denote a space-orienter.
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__init__
(angle1, angle2, angle3, rot_order)[source]¶ Space rotation is similar to Body rotation, but the rotations are applied in the opposite order.
- Parameters
angle1, angle2, angle3 : Expr
Three successive angles to rotate the coordinate system by
rotation_order : string
String defining the order of axes for rotation
Examples
>>> from sympy.vector import CoordSys3D, SpaceOrienter >>> from sympy import symbols >>> q1, q2, q3 = symbols('q1 q2 q3') >>> N = CoordSys3D('N')
To orient a coordinate system D with respect to N, each sequential rotation is always about N’s orthogonal unit vectors. For example, a ‘123’ rotation will specify rotations about N.i, then N.j, then N.k. Therefore,
>>> space_orienter = SpaceOrienter(q1, q2, q3, '312') >>> D = N.orient_new('D', (space_orienter, ))
is same as
>>> from sympy.vector import AxisOrienter >>> axis_orienter1 = AxisOrienter(q1, N.i) >>> B = N.orient_new('B', (axis_orienter1, )) >>> axis_orienter2 = AxisOrienter(q2, N.j) >>> C = B.orient_new('C', (axis_orienter2, )) >>> axis_orienter3 = AxisOrienter(q3, N.k) >>> D = C.orient_new('C', (axis_orienter3, ))
See also
BodyOrienter
Orienter to orient systems wrt Euler angles.
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QuaternionOrienter¶
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class
sympy.vector.orienters.
QuaternionOrienter
(angle1, angle2, angle3, rot_order)[source]¶ Class to denote a quaternion-orienter.
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__init__
(angle1, angle2, angle3, rot_order)[source]¶ Quaternion orientation orients the new CoordSys3D with Quaternions, defined as a finite rotation about lambda, a unit vector, by some amount theta.
This orientation is described by four parameters:
q0 = cos(theta/2)
q1 = lambda_x sin(theta/2)
q2 = lambda_y sin(theta/2)
q3 = lambda_z sin(theta/2)
Quaternion does not take in a rotation order.
- Parameters
q0, q1, q2, q3 : Expr
The quaternions to rotate the coordinate system by
Examples
>>> from sympy.vector import CoordSys3D >>> from sympy import symbols >>> q0, q1, q2, q3 = symbols('q0 q1 q2 q3') >>> N = CoordSys3D('N') >>> from sympy.vector import QuaternionOrienter >>> q_orienter = QuaternionOrienter(q0, q1, q2, q3) >>> B = N.orient_new('B', (q_orienter, ))
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