o 8Va-@sddlmZddlmZmZmZmZmZmZm Z m Z ddl m Z ddlmZddlZGdddeZGdd d eZGd d d eZGd d d eZGdddeZGdddeZddZdS))Basic)sympifyeyesincos rot_axis1 rot_axis2 rot_axis3ImmutableMatrix)cacheit)StrNc@seZdZdZddZdS)Orienterz/ Super-class for all orienter classes. cC|jS)zV The rotation matrix corresponding to this orienter instance. )_parent_orientselfr8/usr/lib/python3/dist-packages/sympy/vector/orienters.pyrotation_matrixszOrienter.rotation_matrixN)__name__ __module__ __qualname____doc__rrrrrr s r csLeZdZdZfddZddZeddZedd Z ed d Z Z S) AxisOrienterz+ Class to denote an axis orienter. cs>t|tjjs tdt|}t|||}||_||_ |S)Nzaxis should be a Vector) isinstancesympyvectorZVector TypeErrorrsuper__new___angle_axis)clsangleaxisobj __class__rrrszAxisOrienter.__new__cCdS)a 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, )) Nr)rr#r$rrr__init__&szAxisOrienter.__init__cCstj|j|}||}|j}td||jt |t d|d |dg|dd|d g|d |ddggt |||j}|j}|S)z The rotation matrix corresponding to this orienter instance. Parameters ========== system : CoordSys3D The coordinate system wrt which the rotation matrix is to be computed r) rrZexpressr$ normalizeZ to_matrixr#rTrMatrixr)rsystemr$Ztheta parent_orientrrrrDs zAxisOrienter.rotation_matrixcCrN)r rrrrr#]zAxisOrienter.anglecCrr2)r!rrrrr$ar3zAxisOrienter.axis) rrrrrr)r rpropertyr#r$ __classcell__rrr&rrs    rcsPeZdZdZfddZeddZeddZedd Zed d Z Z S) ThreeAngleOrienterz3 Super-class for Body and Space orienters. c s<t|tr|j}d}|}t|}t|dkstddd|D}dd|D}dd|D}d|}||vr>td t|d }t|d }t|d } t |}t |}t |}|j rot ||t ||t | |} nt | |t ||t ||} | j } t ||||t|} || _|| _|| _|| _| | _| S) N) Z123Z231Z312Z132Z213Z321Z121Z131Z212Z232Z313Z323r*z%rot_order should be a str of length 3cSg|]}|ddqS)X1replace.0irrr vz.ThreeAngleOrienter.__new__..cSr8)Y2r;r=rrrr@wrAcSr8)Z3r;r=rrrr@xrAr7zInvalid rot_type parameterrr,r+)rr namestrupperlenrjoinintr _in_order_rotr.rr_angle1_angle2_angle3 _rot_orderr) r"angle1angle2angle3 rot_orderZapproved_ordersZoriginal_rot_orderZa1Za2a3r1r%r&rrrksP       zThreeAngleOrienter.__new__cCrr2)rNrrrrrRr3zThreeAngleOrienter.angle1cCrr2)rOrrrrrSr3zThreeAngleOrienter.angle2cCrr2)rPrrrrrTr3zThreeAngleOrienter.angle3cCrr2)rQrrrrrUr3zThreeAngleOrienter.rot_order) rrrrrr4rRrSrTrUr5rrr&rr6fs +   r6c@$eZdZdZdZddZddZdS) BodyOrienterz* Class to denote a body-orienter. TcCt|||||}|Sr2r6rr"rRrSrTrUr%rrrr zBodyOrienter.__new__cCr()a 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') NrrrRrSrTrUrrrr)s7zBodyOrienter.__init__NrrrrrLrr)rrrrrX  rXc@rW) SpaceOrienterz+ Class to denote a space-orienter. FcCrYr2rZr[rrrrr\zSpaceOrienter.__new__cCr()a 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 See Also ======== BodyOrienter : Orienter to orient systems wrt Euler angles. 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, )) Nrr]rrrr)s0zSpaceOrienter.__init__Nr^rrrrr`r_r`csXeZdZdZfddZddZeddZedd Zed d Z ed d Z Z S)QuaternionOrienterz0 Class to denote a quaternion-orienter. cs0t|}t|}t|}t|}t|d|d|d|dd||||d||||gd|||||d|d|d|dd||||gd||||d|||||d|d|d|dgg}|j}t|||||}||_||_||_||_||_ |S)Nr+) rr/r.rr_q0_q1_q2_q3r)r"q0q1q2q3r1r%r&rrr1sF zQuaternionOrienter.__new__cCr()a 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, )) Nrr]rrrr)Ms%zQuaternionOrienter.__init__cCrr2)rbrrrrrftr3zQuaternionOrienter.q0cCrr2)rcrrrrrgxr3zQuaternionOrienter.q1cCrr2)rdrrrrrh|r3zQuaternionOrienter.q2cCrr2)rerrrrrir3zQuaternionOrienter.q3) rrrrrr)r4rfrgrhrir5rrr&rra,s '   racCsF|dkr tt|jS|dkrtt|jS|dkr!tt|jSdS)z)DCM for simple axis 1, 2 or 3 rotations. r,r+r*N)r/rr.rr )r$r#rrrrMsrM)Zsympy.core.basicrrrrrrrrr r r/Zsympy.core.cacher Zsympy.core.symbolr Z sympy.vectorr rr6rXr`rarMrrrrs (   PAF? Y