B ˜‘[$ã@sBddlmZmZddlmZddlmZdgZGdd„deƒZ dS)é)Úprint_functionÚdivision)Úsympify)ÚPointÚParticlec@sŠeZdZdZdd„Zdd„ZeZedd„ƒZej dd„ƒZed d „ƒZ e j d d „ƒZ d d „Z dd„Z dd„Z edd„ƒZej dd„ƒZdS)raûA 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 cCs.t|tƒstdƒ‚||_||_||_d|_dS)NzSupply a valid name.r)Ú isinstanceÚstrÚ TypeErrorÚ_nameÚmassÚpointÚpotential_energy)ÚselfÚnamer r ©rú?lib/python3.7/site-packages/sympy/physics/mechanics/particle.pyÚ__init__)s  zParticle.__init__cCs|jS)N)r )rrrrÚ__str__1szParticle.__str__cCs|jS)zMass of the particle.)Ú_mass)rrrrr 6sz Particle.masscCst|ƒ|_dS)N)rr)rÚvaluerrrr ;scCs|jS)zPoint of the particle.)Ú_point)rrrrr ?szParticle.pointcCst|tƒstdƒ‚||_dS)Nz0Particle point attribute must be a Point object.)rrr r)rÚprrrr Ds cCs|j|j |¡S)aLinear 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 Úvel)rÚframerrrÚlinear_momentumJs zParticle.linear_momentumcCs|j |¡|j|j |¡AS)aAngular 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 Zpos_fromr r)rr rrrrÚangular_momentumls%zParticle.angular_momentumcCs&|jtdƒ|j |¡|j |¡@S)awKinetic 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 é)r rr r)rrrrrÚkinetic_energy“s!zParticle.kinetic_energycCs|jS)awThe 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 )Ú_pe)rrrrr ·szParticle.potential_energycCst|ƒ|_dS)aØUsed 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)rZscalarrrrr ËsN)Ú__name__Ú __module__Ú __qualname__Ú__doc__rrÚ__repr__Úpropertyr Úsetterr rrrr rrrrr s  "'$ N) Z __future__rrZsympy.core.backendrZsympy.physics.vectorrÚ__all__ÚobjectrrrrrÚs