\h.SSKJr SSKJr SSKJrJr SSKJrJ r J r J r SSK J r SSKJr SSKJr SSKr"S S \5r"S S \5r"S S\5r"SS\5r"SS\5r"SS\5rSrg))Basic)sympify)cossin)eye rot_axis1 rot_axis2 rot_axis3)ImmutableDenseMatrix)cacheit)StrNc\rSrSrSrSrSrg)Orienter z' Super-class for all orienter classes. cUR$)z> The rotation matrix corresponding to this orienter instance. )_parent_orientselfs N/var/www/auris/envauris/lib/python3.13/site-packages/sympy/vector/orienters.pyrotation_matrixOrienter.rotation_matrixs """N)__name__ __module__ __qualname____firstlineno____doc__r__static_attributes__rrrrr s #rrcb^\rSrSrSrU4SjrSr\S5r\ S5r \ S5r Sr U=r $) AxisOrienterz# Class to denote an axis orienter. c>[U[RR5(d [ S5e[ U5n[ TU]XU5nXlX#l U$)Nzaxis should be a Vector) isinstancesympyvectorVector TypeErrorrsuper__new___angle_axis)clsangleaxisobj __class__s rr*AxisOrienter.__new__sN$ 3 34456 6goc$/   rcg)aI Axis rotation is a rotation about an arbitrary axis by some angle. The angle is supplied as a SymPy expr scalar, and the axis is supplied as a Vector. Parameters ========== angle : Expr The angle by which the new system is to be rotated axis : Vector The axis around which the rotation has to be performed Examples ======== >>> from sympy.vector import CoordSys3D >>> from sympy import symbols >>> q1 = symbols('q1') >>> N = CoordSys3D('N') >>> from sympy.vector import AxisOrienter >>> orienter = AxisOrienter(q1, N.i + 2 * N.j) >>> B = N.orient_new('B', (orienter, )) Nr)rr.r/s r__init__AxisOrienter.__init__(s8 rc[RRURU5R 5nUR U5nUR n[S5X"R-- [U5-[SUS*US/USSUS*/US*USS//5[U5--X"R--nURnU$)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) r%r&expressr/ normalize to_matrixr.rTrMatrixr)rsystemr/theta parent_orients rrAxisOrienter.rotation_matrixFs||##DIIv6@@B~~f% a&4&&=0CJ>!d1gXtAw!7"&q'1tAwh!7#'7(DGQ!7!9:[U[5(a URnSnUn[U5R 5n[ U5S:Xd [ S5eUVs/sHowRSS5PM nnUVs/sHowRSS5PM nnUVs/sHowRSS 5PM nnS RU5nXE;a [ S 5e[US 5n[US 5n [US5n [U5n[U5n[U5nUR(a$[X5[X5-[X5-n O#[X5[X5-[X5-n U Rn [T U]=XX#[U55n XlX,lX>> from sympy.vector import CoordSys3D, BodyOrienter >>> from sympy import symbols >>> q1, q2, q3 = symbols('q1 q2 q3') >>> N = CoordSys3D('N') A 'Body' fixed rotation is described by three angles and three body-fixed rotation axes. To orient a coordinate system D with respect to N, each sequential rotation is always about the orthogonal unit vectors fixed to D. For example, a '123' rotation will specify rotations about N.i, then D.j, then D.k. (Initially, D.i is same as N.i) Therefore, >>> body_orienter = BodyOrienter(q1, q2, q3, '123') >>> D = N.orient_new('D', (body_orienter, )) is same as >>> from sympy.vector import AxisOrienter >>> axis_orienter1 = AxisOrienter(q1, N.i) >>> D = N.orient_new('D', (axis_orienter1, )) >>> axis_orienter2 = AxisOrienter(q2, D.j) >>> D = D.orient_new('D', (axis_orienter2, )) >>> axis_orienter3 = AxisOrienter(q3, D.k) >>> D = D.orient_new('D', (axis_orienter3, )) Acceptable rotation orders are of length 3, expressed in XYZ or 123, and cannot have a rotation about about an axis twice in a row. >>> body_orienter1 = BodyOrienter(q1, q2, q3, '123') >>> body_orienter2 = BodyOrienter(q1, q2, 0, 'ZXZ') >>> body_orienter3 = BodyOrienter(0, 0, 0, 'XYX') Nrrrorprqrrs rr4BodyOrienter.__init__sn rrN rrrrrrir*r4rrrrrrsI 7 rrc(\rSrSrSrSrSrSrSrg) SpaceOrienterz# Class to denote a space-orienter. Fc4[RXX#U5nU$rDrrs rr*SpaceOrienter.__new__rrcg)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, )) Nrrs rr4SpaceOrienter.__init__s` rrNrrrrrrsI 0 rrcr^\rSrSrSrU4SjrSr\S5r\S5r \S5r \S5r S r U=r $) QuaternionOrienteri.z( Class to denote a quaternion-orienter. c >[U5n[U5n[U5n[U5n[US-US--US-- US-- SX#-X-- -SX-X$---/SX#-X---US-US-- US--US-- SX4-X-- -/SX$-X-- -SX-X4---US-US-- US-- US--//5nURn[TU]XX#U5nXlX&lX6lXFlXVl U$)Nr8) rr>r=r)r*_q0_q1_q2_q3r)r-q0q1q2q3rAr0r1s rr*QuaternionOrienter.__new__3s_ R[ R[ R[ R["'B!G"3bAg"="$'#*"#rw'8"9"#rw'8"9";#$rw'8"9"$'B!G"3"$'#*,.!G#4"#rw'8"9";#$rw'8"9"#rw'8"9"$'B!G"3"$'#*,.!G#4"5 !6 7 & gocrr2* rcg)a Quaternion orientation orients the new CoordSys3D with Quaternions, defined as a finite rotation about lambda, a unit vector, by some amount theta. This orientation is described by four parameters: q0 = cos(theta/2) q1 = lambda_x sin(theta/2) q2 = lambda_y sin(theta/2) q3 = lambda_z sin(theta/2) Quaternion does not take in a rotation order. Parameters ========== q0, q1, q2, q3 : Expr The quaternions to rotate the coordinate system by Examples ======== >>> from sympy.vector import CoordSys3D >>> from sympy import symbols >>> q0, q1, q2, q3 = symbols('q0 q1 q2 q3') >>> N = CoordSys3D('N') >>> from sympy.vector import QuaternionOrienter >>> q_orienter = QuaternionOrienter(q0, q1, q2, q3) >>> B = N.orient_new('B', (q_orienter, )) Nrrs rr4QuaternionOrienter.__init__OsJ rcUR$rD)rrs rrQuaternionOrienter.q0v xxrcUR$rD)rrs rrQuaternionOrienter.q1zrrcUR$rD)rrs rrQuaternionOrienter.q2~rrcUR$rD)rrs rrQuaternionOrienter.q3rrr)rrrrrr*r4rHrrrrrrIrJs@rrr.sc8% NrrcUS:Xa[[U5R5$US:Xa[[U5R5$US:Xa[[ U5R5$g)z)DCM for simple axis 1, 2 or 3 rotations. r9r8r7N)r>rr=r r )r/r.s rrjrjs^ qyi&(()) i&(()) i&(()) r)sympy.core.basicrsympy.core.sympifyr(sympy.functions.elementary.trigonometricrrsympy.matrices.denserrr r sympy.matrices.immutabler r>sympy.core.cacher sympy.core.symbolr sympy.vectorr%rr!rLrrrrjrrrrsz"&?GGC$! #u #M8M`>>BC %C L< &< ~VVr*r