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| from sympy import S | |
| from sympy.physics.vector import cross, dot | |
| from sympy.physics.mechanics.body_base import BodyBase | |
| from sympy.physics.mechanics.inertia import inertia_of_point_mass | |
| from sympy.utilities.exceptions import sympy_deprecation_warning | |
| __all__ = ['Particle'] | |
| class Particle(BodyBase): | |
| """A 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 | |
| potential_energy : Sympifyable | |
| The potential energy of the Particle. | |
| 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 | |
| """ | |
| point = BodyBase.masscenter | |
| def __init__(self, name, point=None, mass=None): | |
| super().__init__(name, point, mass) | |
| def linear_momentum(self, frame): | |
| """Linear 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 | |
| """ | |
| return self.mass * self.point.vel(frame) | |
| def angular_momentum(self, point, frame): | |
| """Angular 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 | |
| """ | |
| return cross(self.point.pos_from(point), | |
| self.mass * self.point.vel(frame)) | |
| def kinetic_energy(self, frame): | |
| """Kinetic 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 | |
| """ | |
| return S.Half * self.mass * dot(self.point.vel(frame), | |
| self.point.vel(frame)) | |
| def set_potential_energy(self, scalar): | |
| sympy_deprecation_warning( | |
| """ | |
| The sympy.physics.mechanics.Particle.set_potential_energy() | |
| method is deprecated. Instead use | |
| P.potential_energy = scalar | |
| """, | |
| deprecated_since_version="1.5", | |
| active_deprecations_target="deprecated-set-potential-energy", | |
| ) | |
| self.potential_energy = scalar | |
| def parallel_axis(self, point, frame): | |
| """Returns 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. | |
| """ | |
| return inertia_of_point_mass(self.mass, self.point.pos_from(point), | |
| frame) | |