class_docstr: 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
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docstr: 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
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code: 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))
      )
  
file_path: sympy/sympy/physics/mechanics/particle.py
imports: 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
label_desc: Use image node_id 4 for calling the Particle obj's underlying member method code with example usage: obj.kinetic_energy(frame) and returns: unknown