MZdBddlmZddlmZddlmZdgZGddZy))sympify)Point)sympy_deprecation_warningParticleceZdZdZdZdZdZedZejdZedZ e jdZ d Z d Z d Z ed Zejd ZdZdZy)raA particle. Explanation =========== 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 crt|ts td||_||_||_d|_y)NzSupply a valid name.r) isinstancestr TypeError_namemasspointpotential_energy)selfnamerr s B/usr/lib/python3/dist-packages/sympy/physics/mechanics/particle.py__init__zParticle.__init__-s5$$23 3   !c|jSN)r rs r__str__zParticle.__str__5s zzrc"|jSr)rrs r__repr__zParticle.__repr__8s||~rc|jS)zMass of the particle.)_massrs rr z Particle.mass;szzrc$t||_yr)rr)rvalues rr z Particle.mass@s U^ rc|jS)zPoint of the particle.)_pointrs rrzParticle.pointDs{{rcHt|ts td||_y)Nz0Particle point attribute must be a Point object.)r rr r )rps rrzParticle.pointIs!U#NO O rcR|j|jj|zS)aLinear momentum of the particle. Explanation =========== 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 >>> from sympy.physics.vector import init_vprinting >>> init_vprinting(pretty_print=False) >>> 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 rvelrframes rlinear_momentumzParticle.linear_momentumOs!Jyy4::>>%000rc|jj||j|jj|zz S)aAngular momentum of the particle about the point. Explanation =========== The angular momentum H, about some point O of a particle, P, is given by: ``H = cross(r, 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 >>> from sympy.physics.vector import init_vprinting >>> init_vprinting(pretty_print=False) >>> 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 )rpos_fromr r$)rrr&s rangular_momentumzParticle.angular_momentumvs5Tzz""5)TYY9N-NOOrc|jtdz |jj|z|jj|zS)aKinetic energy of the particle. Explanation =========== The kinetic energy, T, of a particle, P, is given by: ``T = 1/2 (dot(m * v, v))`` 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 )r rrr$r%s rkinetic_energyzParticle.kinetic_energysAH GAJ&)>> u%& 'rc|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 )_pers rrzParticle.potential_energys $xxrc$t||_y)aUsed 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/rscalars rrzParticle.potential_energys,6?rc.tddd||_y)Nz The sympy.physics.mechanics.Particle.set_potential_energy() method is deprecated. Instead use P.potential_energy = scalar z1.5zdeprecated-set-potential-energy)deprecated_since_versionactive_deprecations_target)rrr1s rset_potential_energyzParticle.set_potential_energys!!  "'#D !'rchddlm}||j|jj ||S)aReturns an inertia dyadic of the particle with respect to another point and frame. Parameters ========== point : sympy.physics.vector.Point The point to express the inertia dyadic about. frame : sympy.physics.vector.ReferenceFrame The reference frame used to construct the dyadic. Returns ======= inertia : sympy.physics.vector.Dyadic The inertia dyadic of the particle expressed about the provided point and frame. r)inertia_of_point_mass)sympy.physics.mechanicsr8r rr))rrr&r8s r parallel_axiszParticle.parallel_axiss/* B$TYY 0C0CE0J%*, ,rN)__name__ __module__ __qualname____doc__rrrpropertyr setterrr'r*r-rr6r:rrrr s!F" [[$$ \\ %1N*PX%'N&##. ',rN)sympy.core.backendrsympy.physics.vectorrsympy.utilities.exceptionsr__all__rrArrrFs!&&@ ,P,P,r