# Source code for sympy.physics.mechanics.particle

```
from __future__ import print_function, division
from sympy.core.backend import sympify
from sympy.core.compatibility import string_types
from sympy.physics.vector import Point
__all__ = ['Particle']
[docs]class Particle(object):
"""A 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
"""
def __init__(self, name, point, mass):
if not isinstance(name, string_types):
raise TypeError('Supply a valid name.')
self._name = name
self.mass = mass
self.point = point
self.potential_energy = 0
def __str__(self):
return self._name
__repr__ = __str__
@property
def mass(self):
"""Mass of the particle."""
return self._mass
@mass.setter
def mass(self, value):
self._mass = sympify(value)
@property
def point(self):
"""Point of the particle."""
return self._point
@point.setter
def point(self, p):
if not isinstance(p, Point):
raise TypeError("Particle point attribute must be a Point object.")
self._point = p
[docs] def linear_momentum(self, frame):
"""Linear 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
"""
return self.mass * self.point.vel(frame)
[docs] def angular_momentum(self, point, frame):
"""Angular 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
"""
return self.point.pos_from(point) ^ (self.mass * self.point.vel(frame))
[docs] def kinetic_energy(self, frame):
"""Kinetic 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
"""
return (self.mass / sympify(2) * self.point.vel(frame) &
self.point.vel(frame))
@property
def potential_energy(self):
"""The 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
"""
return self._pe
@potential_energy.setter
def potential_energy(self, scalar):
"""Used 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
"""
self._pe = sympify(scalar)
```