/

Source code for sympy.physics.mechanics.body

from sympy import Symbol
from sympy.physics.mechanics import (RigidBody, Particle, ReferenceFrame,
                                     inertia)
from sympy.physics.vector import Point, Vector

__all__ = ['Body']


[docs]class Body(RigidBody, Particle): """ Body is a common representation of RigidBody or a Particle. A Body represents either a rigid body or particle in classical mechanics. Bodies have a body-fixed reference frame, a mass, a mass center and possibly a body-fixed inertia. Parameters ---------- name: String Defines the name of the body. It is used as the base for defining body specific properties. masscenter : Point, optional A point that represents the center of mass of the body or particle. If no point is given, a point is generated. frame : ReferenceFrame (optional) The ReferenceFrame that represents the reference frame of the body. If no frame is given, a frame is generated. mass : Sympifyable, optional A Sympifyable object which represents the mass of the body. if no mass is passed, one is generated. body_inertia : Dyadic Central inertia dyadic of the body. If none is passed while creating RigidBody, a default inertia is generated. Examples -------- Default behaviour. It creates a RigidBody after defining mass, mass center, frame and inertia. >>> from sympy.physics.mechanics import Body >>> body = Body('name_of_body') Passing attributes of Rigidbody. All the arguments needed to create a RigidBody can be passed while creating a Body too. >>> from sympy import Symbol >>> from sympy.physics.mechanics import ReferenceFrame, Point, inertia >>> from sympy.physics.mechanics import Body >>> mass = Symbol('mass') >>> masscenter = Point('masscenter') >>> frame = ReferenceFrame('frame') >>> ixx = Symbol('ixx') >>> body_inertia = inertia(frame, ixx, 0, 0) >>> body = Body('name_of_body',masscenter,mass,frame,body_inertia) Creating a Particle. If masscenter and mass are passed, and inertia is not then a Particle is created. >>> from sympy import Symbol >>> from sympy.physics.vector import Point >>> from sympy.physics.mechanics import Body >>> mass = Symbol('mass') >>> masscenter = Point('masscenter') >>> body = Body('name_of_body',masscenter,mass) Similarly, A frame can also be passed while creating a Particle. """ def __init__(self, name, masscenter=None, mass=None, frame=None, central_inertia=None): self.name = name self.loads = [] if frame is None: frame = ReferenceFrame(name + '_frame') if masscenter is None: masscenter = Point(name + '_masscenter') if central_inertia is None and mass is None: ixx = Symbol(name + '_ixx') iyy = Symbol(name + '_iyy') izz = Symbol(name + '_izz') izx = Symbol(name + '_izx') ixy = Symbol(name + '_ixy') iyz = Symbol(name + '_iyz') _inertia = (inertia(frame, ixx, iyy, izz, ixy, iyz, izx), masscenter) else: _inertia = (central_inertia, masscenter) if mass is None: _mass = Symbol(name + '_mass') else: _mass = mass masscenter.set_vel(frame, 0) # If user passes masscenter and mass then a particle is created # otherwise a rigidbody. As a result a body may or may not have inertia. if central_inertia is None and mass is not None: self.frame = frame self.masscenter = masscenter Particle.__init__(self, name, masscenter, _mass) else: RigidBody.__init__(self, name, masscenter, frame, _mass, _inertia)
[docs] def apply_force(self, vec, point=None): """ Adds the force to the point (center of mass by default) on the body. Parameters ---------- vec: Vector Defines the force vector. Can be any vector w.r.t any frame or combinations of frame. point: Point, optional Defines the point on which the force must be applied. Default is Body's center of mass. Example ------- To apply a unit force in x direction of body's frame to body's center of mass. >>> from sympy import Symbol >>> from sympy.physics.mechanics import Body >>> body = Body('body') >>> g = Symbol('g') >>> body.apply_force(body.mass * g * body.frame.x) To apply force to any other point than center of mass, pass that point as well. >>> from sympy import Symbol >>> from sympy.physics.mechanics import Body >>> parent = Body('parent') >>> child = Body('child') >>> g = Symbol('g') >>> frame = parent.frame >>> l = Symbol('l') >>> point = child.masscenter.locatenew('force_point', l * body.frame.y) >>> gravity = child.mass * g >>> body.apply_force(gravity * body.frame.x, point) """ if not isinstance(point, Point): if point is None: point = self.masscenter # masscenter else: raise TypeError("A Point must be supplied to apply force to.") if not isinstance(vec, Vector): raise TypeError("A Vector must be supplied to apply force.") self.loads.append((point, vec))
[docs] def apply_torque(self, vec): """ Adds torque to the body. Parameters ---------- vec: Vector Defines the torque vector. Can be any vector w.r.t any frame or combinations of frame. """ if not isinstance(vec, Vector): raise TypeError("A Vector must be supplied to add torque.") self.loads.append((self.frame, vec))