ó ¡¼™\c@ suddlmZmZddlmZmZddlmZmZddl m Z dgZ de fd„ƒYZ dS( iÿÿÿÿ(tprint_functiontdivision(tranget string_typesi(tVectort _check_vector(t _check_frametPointcB s¤eZdZd„Zd„ZeZd„Zd„Zd„Zd„Z d„Z d„Z d „Z d „Z d „Zd „Zd „Zd„Zd„Zd„ZRS(sáThis object represents a point in a dynamic system. It stores the: position, velocity, and acceleration of a point. The position is a vector defined as the vector distance from a parent point to this point. cC sC||_i|_i|_i|_|j|j|jg|_dS(s"Initialization of a Point object. N(tnamet _pos_dictt _vel_dictt _acc_dictt_pdlist(tselfR((s9lib/python2.7/site-packages/sympy/physics/vector/point.pyt__init__s     cC s|jS(N(R(R ((s9lib/python2.7/site-packages/sympy/physics/vector/point.pyt__str__scC s"t|tƒstdƒ‚ndS(NsA Point must be supplied(t isinstanceRt TypeError(R tother((s9lib/python2.7/site-packages/sympy/physics/vector/point.pyt _check_pointsc C sG|gg}gg}x¦||kr½|}xŒt|ƒD]~\}}|dj|jƒ}xXt|ƒD]J\}} |j| ƒsh|| g} |j| ƒs²|j| ƒq²qhqhWq8WqWx:t|ƒD],\}}|d|krË|j|ƒqËqËW|jdtƒt|ƒdkr%|dStd|j d|j ƒ‚dS(s3Creates a list from self to other using _dcm_dict. iÿÿÿÿtkeyis!No Connecting Path found between s and N( t enumerateR tkeyst __contains__tappendtremovetsorttlent ValueErrorR( R Rtnumtoutlisttoldlisttitvttemplistti2tv2tlittletemplist((s9lib/python2.7/site-packages/sympy/physics/vector/point.pyt _pdict_list#s&   c C s¼t|ƒt|ƒ|j|ƒ|j|ƒ}|j|ƒ}|j|ƒ}|j|ƒ}|j|ƒ}|j|ƒ} |j||d||A|| |A|||AAƒ|j|ƒS(sESets the acceleration of this point with the 1-point theory. The 1-point theory for point acceleration looks like this: ^N a^P = ^B a^P + ^N a^O + ^N alpha^B x r^OP + ^N omega^B x (^N omega^B x r^OP) + 2 ^N omega^B x ^B v^P where O is a point fixed in B, P is a point moving in B, and B is rotating in frame N. Parameters ========== otherpoint : Point The first point of the 1-point theory (O) outframe : ReferenceFrame The frame we want this point's acceleration defined in (N) fixedframe : ReferenceFrame The intermediate frame in this calculation (B) Examples ======== >>> from sympy.physics.vector import Point, ReferenceFrame >>> from sympy.physics.vector import Vector, dynamicsymbols >>> q = dynamicsymbols('q') >>> q2 = dynamicsymbols('q2') >>> qd = dynamicsymbols('q', 1) >>> q2d = dynamicsymbols('q2', 1) >>> N = ReferenceFrame('N') >>> B = ReferenceFrame('B') >>> B.set_ang_vel(N, 5 * B.y) >>> O = Point('O') >>> P = O.locatenew('P', q * B.x) >>> P.set_vel(B, qd * B.x + q2d * B.y) >>> O.set_vel(N, 0) >>> P.a1pt_theory(O, N, B) (-25*q + q'')*B.x + q2''*B.y - 10*q'*B.z i(RRtpos_fromtveltacct ang_vel_int ang_acc_intset_acc( R t otherpointtoutframet interframetdistR!ta1ta2tomegatalpha((s9lib/python2.7/site-packages/sympy/physics/vector/point.pyt a1pt_theory9s*   $cC sŽt|ƒt|ƒ|j|ƒ|j|ƒ}|j|ƒ}|j|ƒ}|j|ƒ}|j||||A|||AAƒ|j|ƒS(sASets the acceleration of this point with the 2-point theory. The 2-point theory for point acceleration looks like this: ^N a^P = ^N a^O + ^N alpha^B x r^OP + ^N omega^B x (^N omega^B x r^OP) where O and P are both points fixed in frame B, which is rotating in frame N. Parameters ========== otherpoint : Point The first point of the 2-point theory (O) outframe : ReferenceFrame The frame we want this point's acceleration defined in (N) fixedframe : ReferenceFrame The frame in which both points are fixed (B) Examples ======== >>> from sympy.physics.vector import Point, ReferenceFrame, dynamicsymbols >>> q = dynamicsymbols('q') >>> qd = dynamicsymbols('q', 1) >>> N = ReferenceFrame('N') >>> B = N.orientnew('B', 'Axis', [q, N.z]) >>> O = Point('O') >>> P = O.locatenew('P', 10 * B.x) >>> O.set_vel(N, 5 * N.x) >>> P.a2pt_theory(O, N, B) - 10*q'**2*B.x + 10*q''*B.y (RRR'R)R*R+R,(R R-R.t fixedframeR0taR3R4((s9lib/python2.7/site-packages/sympy/physics/vector/point.pyt a2pt_theoryps$   $cC sXt|ƒ||jkrM|j|dkr@|j|j|ƒStdƒSn|j|S(sÏThe acceleration Vector of this Point in a ReferenceFrame. Parameters ========== frame : ReferenceFrame The frame in which the returned acceleration vector will be defined in Examples ======== >>> from sympy.physics.vector import Point, ReferenceFrame >>> N = ReferenceFrame('N') >>> p1 = Point('p1') >>> p1.set_acc(N, 10 * N.x) >>> p1.acc(N) 10*N.x i(RR R tdtR(R tframe((s9lib/python2.7/site-packages/sympy/physics/vector/point.pyR)žs   cC svt|tƒstdƒ‚n|dkr9tdƒ}nt|ƒ}t|ƒ}|j||ƒ|j|| ƒ|S(sÖCreates a new point with a position defined from this point. Parameters ========== name : str The name for the new point value : Vector The position of the new point relative to this point Examples ======== >>> from sympy.physics.vector import ReferenceFrame, Point >>> N = ReferenceFrame('N') >>> P1 = Point('P1') >>> P2 = P1.locatenew('P2', 10 * N.x) sMust supply a valid namei(RRRRRRtset_pos(R Rtvaluetp((s9lib/python2.7/site-packages/sympy/physics/vector/point.pyt locatenew»s   cC s`tdƒ}|j|dƒ}x;tt|ƒdƒD]#}|||j||d7}q5W|S(sãReturns a Vector distance between this Point and the other Point. Parameters ========== otherpoint : Point The otherpoint we are locating this one relative to Examples ======== >>> from sympy.physics.vector import Point, ReferenceFrame >>> N = ReferenceFrame('N') >>> p1 = Point('p1') >>> p2 = Point('p2') >>> p1.set_pos(p2, 10 * N.x) >>> p1.pos_from(p2) 10*N.x ii(RR&RRR (R R-toutvectplistR ((s9lib/python2.7/site-packages/sympy/physics/vector/point.pyR'Ús  !cC sL|dkrtdƒ}nt|ƒ}t|ƒ|jji||6ƒdS(s#Used to set the acceleration of this Point in a ReferenceFrame. Parameters ========== frame : ReferenceFrame The frame in which this point's acceleration is defined value : Vector The vector value of this point's acceleration in the frame Examples ======== >>> from sympy.physics.vector import Point, ReferenceFrame >>> N = ReferenceFrame('N') >>> p1 = Point('p1') >>> p1.set_acc(N, 10 * N.x) >>> p1.acc(N) 10*N.x iN(RRRR tupdate(R R:R<((s9lib/python2.7/site-packages/sympy/physics/vector/point.pyR,ös    cC sg|dkrtdƒ}nt|ƒ}|j|ƒ|jji||6ƒ|jji| |6ƒdS(sDUsed to set the position of this point w.r.t. another point. Parameters ========== otherpoint : Point The other point which this point's location is defined relative to value : Vector The vector which defines the location of this point Examples ======== >>> from sympy.physics.vector import Point, ReferenceFrame >>> N = ReferenceFrame('N') >>> p1 = Point('p1') >>> p2 = Point('p2') >>> p1.set_pos(p2, 10 * N.x) >>> p1.pos_from(p2) 10*N.x iN(RRRR RA(R R-R<((s9lib/python2.7/site-packages/sympy/physics/vector/point.pyR;s    cC sL|dkrtdƒ}nt|ƒ}t|ƒ|jji||6ƒdS(sSets the velocity Vector of this Point in a ReferenceFrame. Parameters ========== frame : ReferenceFrame The frame in which this point's velocity is defined value : Vector The vector value of this point's velocity in the frame Examples ======== >>> from sympy.physics.vector import Point, ReferenceFrame >>> N = ReferenceFrame('N') >>> p1 = Point('p1') >>> p1.set_vel(N, 10 * N.x) >>> p1.vel(N) 10*N.x iN(RRRR RA(R R:R<((s9lib/python2.7/site-packages/sympy/physics/vector/point.pytset_vel2s    cC s†t|ƒt|ƒ|j|ƒ|j|ƒ}|j|ƒ}|j|ƒ}|j|ƒ}|j|||||Aƒ|j|ƒS(sèSets the velocity of this point with the 1-point theory. The 1-point theory for point velocity looks like this: ^N v^P = ^B v^P + ^N v^O + ^N omega^B x r^OP where O is a point fixed in B, P is a point moving in B, and B is rotating in frame N. Parameters ========== otherpoint : Point The first point of the 2-point theory (O) outframe : ReferenceFrame The frame we want this point's velocity defined in (N) interframe : ReferenceFrame The intermediate frame in this calculation (B) Examples ======== >>> from sympy.physics.vector import Point, ReferenceFrame >>> from sympy.physics.vector import Vector, dynamicsymbols >>> q = dynamicsymbols('q') >>> q2 = dynamicsymbols('q2') >>> qd = dynamicsymbols('q', 1) >>> q2d = dynamicsymbols('q2', 1) >>> N = ReferenceFrame('N') >>> B = ReferenceFrame('B') >>> B.set_ang_vel(N, 5 * B.y) >>> O = Point('O') >>> P = O.locatenew('P', q * B.x) >>> P.set_vel(B, qd * B.x + q2d * B.y) >>> O.set_vel(N, 0) >>> P.v1pt_theory(O, N, B) q'*B.x + q2'*B.y - 5*q*B.z (RRR'R(R*RB(R R-R.R/R0tv1R$R3((s9lib/python2.7/site-packages/sympy/physics/vector/point.pyt v1pt_theoryOs)   cC sst|ƒt|ƒ|j|ƒ|j|ƒ}|j|ƒ}|j|ƒ}|j||||Aƒ|j|ƒS(sSets the velocity of this point with the 2-point theory. The 2-point theory for point velocity looks like this: ^N v^P = ^N v^O + ^N omega^B x r^OP where O and P are both points fixed in frame B, which is rotating in frame N. Parameters ========== otherpoint : Point The first point of the 2-point theory (O) outframe : ReferenceFrame The frame we want this point's velocity defined in (N) fixedframe : ReferenceFrame The frame in which both points are fixed (B) Examples ======== >>> from sympy.physics.vector import Point, ReferenceFrame, dynamicsymbols >>> q = dynamicsymbols('q') >>> qd = dynamicsymbols('q', 1) >>> N = ReferenceFrame('N') >>> B = N.orientnew('B', 'Axis', [q, N.z]) >>> O = Point('O') >>> P = O.locatenew('P', 10 * B.x) >>> O.set_vel(N, 5 * N.x) >>> P.v2pt_theory(O, N, B) 5*N.x + 10*q'*B.y (RRR'R(R*RB(R R-R.R6R0R!R3((s9lib/python2.7/site-packages/sympy/physics/vector/point.pyt v2pt_theory‚s$   cC sEt|ƒ||jkr:td|jd|jƒ‚n|j|S(sÉThe velocity Vector of this Point in the ReferenceFrame. Parameters ========== frame : ReferenceFrame The frame in which the returned velocity vector will be defined in Examples ======== >>> from sympy.physics.vector import Point, ReferenceFrame >>> N = ReferenceFrame('N') >>> p1 = Point('p1') >>> p1.set_vel(N, 10 * N.x) >>> p1.vel(N) 10*N.x sVelocity of point s( has not been defined in ReferenceFrame (RR RR(R R:((s9lib/python2.7/site-packages/sympy/physics/vector/point.pyR(¯s  cG s\g|D]'}|j|ƒj||dtƒ^q}t|ƒdkrN|dSt|ƒSdS(sReturns the partial velocities of the linear velocity vector of this point in the given frame with respect to one or more provided generalized speeds. Parameters ========== frame : ReferenceFrame The frame with which the velocity is defined in. gen_speeds : functions of time The generalized speeds. Returns ======= partial_velocities : tuple of Vector The partial velocity vectors corresponding to the provided generalized speeds. Examples ======== >>> from sympy.physics.vector import ReferenceFrame, Point >>> from sympy.physics.vector import dynamicsymbols >>> N = ReferenceFrame('N') >>> A = ReferenceFrame('A') >>> p = Point('p') >>> u1, u2 = dynamicsymbols('u1, u2') >>> p.set_vel(N, u1 * N.x + u2 * A.y) >>> p.partial_velocity(N, u1) N.x >>> p.partial_velocity(N, u1, u2) (N.x, A.y) t var_in_dcmiiN(R(tdifftFalseRttuple(R R:t gen_speedstspeedtpartials((s9lib/python2.7/site-packages/sympy/physics/vector/point.pytpartial_velocityÊs "1(t__name__t __module__t__doc__RRt__repr__RR&R5R8R)R>R'R,R;RBRDRER(RM(((s9lib/python2.7/site-packages/sympy/physics/vector/point.pyR s$     7 .       3 - N(t __future__RRtsympy.core.compatibilityRRtvectorRRR:Rt__all__tobjectR(((s9lib/python2.7/site-packages/sympy/physics/vector/point.pyts