ó ¡¼™\c@ siddlmZmZddlmZddlmZddlmZdgZ de fd„ƒYZ dS(iÿÿÿÿ(tprint_functiontdivision(tsympify(t string_types(tPointtParticlecB s¤eZdZd„Zd„ZeZed„ƒZejd„ƒZed„ƒZ e jd„ƒZ d„Z d„Z d „Z ed „ƒZ e jd „ƒZ RS( sûA particle. Particles have a non-zero mass and lack spatial extension; they take up no space. Values need to be supplied on initialization, but can be changed later. Parameters ========== name : str Name of particle point : Point A physics/mechanics Point which represents the position, velocity, and acceleration of this Particle mass : sympifyable A SymPy expression representing the Particle's mass Examples ======== >>> from sympy.physics.mechanics import Particle, Point >>> from sympy import Symbol >>> po = Point('po') >>> m = Symbol('m') >>> pa = Particle('pa', po, m) >>> # Or you could change these later >>> pa.mass = m >>> pa.point = po cC sFt|tƒstdƒ‚n||_||_||_d|_dS(NsSupply a valid name.i(t isinstanceRt TypeErrort_nametmasstpointtpotential_energy(tselftnameR R ((s?lib/python2.7/site-packages/sympy/physics/mechanics/particle.pyt__init__*s    cC s|jS(N(R(R ((s?lib/python2.7/site-packages/sympy/physics/mechanics/particle.pyt__str__2scC s|jS(sMass of the particle.(t_mass(R ((s?lib/python2.7/site-packages/sympy/physics/mechanics/particle.pyR 7scC st|ƒ|_dS(N(RR(R tvalue((s?lib/python2.7/site-packages/sympy/physics/mechanics/particle.pyR <scC s|jS(sPoint of the particle.(t_point(R ((s?lib/python2.7/site-packages/sympy/physics/mechanics/particle.pyR @scC s+t|tƒstdƒ‚n||_dS(Ns0Particle point attribute must be a Point object.(RRRR(R tp((s?lib/python2.7/site-packages/sympy/physics/mechanics/particle.pyR EscC s|j|jj|ƒS(sLinear momentum of the particle. The linear momentum L, of a particle P, with respect to frame N is given by L = m * v where m is the mass of the particle, and v is the velocity of the particle in the frame N. Parameters ========== frame : ReferenceFrame The frame in which linear momentum is desired. Examples ======== >>> from sympy.physics.mechanics import Particle, Point, ReferenceFrame >>> from sympy.physics.mechanics import dynamicsymbols >>> m, v = dynamicsymbols('m v') >>> N = ReferenceFrame('N') >>> P = Point('P') >>> A = Particle('A', P, m) >>> P.set_vel(N, v * N.x) >>> A.linear_momentum(N) m*v*N.x (R R tvel(R tframe((s?lib/python2.7/site-packages/sympy/physics/mechanics/particle.pytlinear_momentumKs cC s'|jj|ƒ|j|jj|ƒAS(sAngular momentum of the particle about the point. The angular momentum H, about some point O of a particle, P, is given by: H = r x m * v where r is the position vector from point O to the particle P, m is the mass of the particle, and v is the velocity of the particle in the inertial frame, N. Parameters ========== point : Point The point about which angular momentum of the particle is desired. frame : ReferenceFrame The frame in which angular momentum is desired. Examples ======== >>> from sympy.physics.mechanics import Particle, Point, ReferenceFrame >>> from sympy.physics.mechanics import dynamicsymbols >>> m, v, r = dynamicsymbols('m v r') >>> N = ReferenceFrame('N') >>> O = Point('O') >>> A = O.locatenew('A', r * N.x) >>> P = Particle('P', A, m) >>> P.point.set_vel(N, v * N.y) >>> P.angular_momentum(O, N) m*r*v*N.z (R tpos_fromR R(R R R((s?lib/python2.7/site-packages/sympy/physics/mechanics/particle.pytangular_momentumms%cC s1|jtdƒ|jj|ƒ|jj|ƒ@S(swKinetic energy of the particle The kinetic energy, T, of a particle, P, is given by 'T = 1/2 m v^2' where m is the mass of particle P, and v is the velocity of the particle in the supplied ReferenceFrame. Parameters ========== frame : ReferenceFrame The Particle's velocity is typically defined with respect to an inertial frame but any relevant frame in which the velocity is known can be supplied. Examples ======== >>> from sympy.physics.mechanics import Particle, Point, ReferenceFrame >>> from sympy import symbols >>> m, v, r = symbols('m v r') >>> N = ReferenceFrame('N') >>> O = Point('O') >>> P = Particle('P', O, m) >>> P.point.set_vel(N, v * N.y) >>> P.kinetic_energy(N) m*v**2/2 i(R RR R(R R((s?lib/python2.7/site-packages/sympy/physics/mechanics/particle.pytkinetic_energy”s! cC s|jS(swThe potential energy of the Particle. Examples ======== >>> from sympy.physics.mechanics import Particle, Point >>> from sympy import symbols >>> m, g, h = symbols('m g h') >>> O = Point('O') >>> P = Particle('P', O, m) >>> P.potential_energy = m * g * h >>> P.potential_energy g*h*m (t_pe(R ((s?lib/python2.7/site-packages/sympy/physics/mechanics/particle.pyR ¸scC st|ƒ|_dS(sØUsed to set the potential energy of the Particle. Parameters ========== scalar : Sympifyable The potential energy (a scalar) of the Particle. Examples ======== >>> from sympy.physics.mechanics import Particle, Point >>> from sympy import symbols >>> m, g, h = symbols('m g h') >>> O = Point('O') >>> P = Particle('P', O, m) >>> P.potential_energy = m * g * h N(RR(R tscalar((s?lib/python2.7/site-packages/sympy/physics/mechanics/particle.pyR Ìs(t__name__t __module__t__doc__RRt__repr__tpropertyR tsetterR RRRR (((s?lib/python2.7/site-packages/sympy/physics/mechanics/particle.pyR s   " ' $N( t __future__RRtsympy.core.backendRtsympy.core.compatibilityRtsympy.physics.vectorRt__all__tobjectR(((s?lib/python2.7/site-packages/sympy/physics/mechanics/particle.pyts