Beispiel #1
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def test_body_add_force():
    # Body with RigidBody.
    rigidbody_masscenter = Point('rigidbody_masscenter')
    rigidbody_mass = Symbol('rigidbody_mass')
    rigidbody_frame = ReferenceFrame('rigidbody_frame')
    body_inertia = inertia(rigidbody_frame, 1, 0, 0)
    rigid_body = Body('rigidbody_body', rigidbody_masscenter, rigidbody_mass,
                      rigidbody_frame, body_inertia)

    l = Symbol('l')
    Fa = Symbol('Fa')
    point = rigid_body.masscenter.locatenew('rigidbody_body_point0',
                                            l * rigid_body.frame.x)
    point.set_vel(rigid_body.frame, 0)
    force_vector = Fa * rigid_body.frame.z
    # apply_force with point
    rigid_body.apply_force(force_vector, point)
    assert len(rigid_body.loads) == 1
    force_point = rigid_body.loads[0][0]
    frame = rigid_body.frame
    assert force_point.vel(frame) == point.vel(frame)
    assert force_point.pos_from(force_point) == point.pos_from(force_point)
    assert rigid_body.loads[0][1] == force_vector
    # apply_force without point
    rigid_body.apply_force(force_vector)
    assert len(rigid_body.loads) == 2
    assert rigid_body.loads[1][1] == force_vector
    # passing something else than point
    raises(TypeError, lambda: rigid_body.apply_force(force_vector, 0))
    raises(TypeError, lambda: rigid_body.apply_force(0))
Beispiel #2
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def test_custom_rigid_body():
    # Body with RigidBody.
    rigidbody_masscenter = Point("rigidbody_masscenter")
    rigidbody_mass = Symbol("rigidbody_mass")
    rigidbody_frame = ReferenceFrame("rigidbody_frame")
    body_inertia = inertia(rigidbody_frame, 1, 0, 0)
    rigid_body = Body(
        "rigidbody_body",
        rigidbody_masscenter,
        rigidbody_mass,
        rigidbody_frame,
        body_inertia,
    )
    com = rigid_body.masscenter
    frame = rigid_body.frame
    rigidbody_masscenter.set_vel(rigidbody_frame, 0)
    assert com.vel(frame) == rigidbody_masscenter.vel(frame)
    assert com.pos_from(com) == rigidbody_masscenter.pos_from(com)

    assert rigid_body.mass == rigidbody_mass
    assert rigid_body.inertia == (body_inertia, rigidbody_masscenter)

    assert hasattr(rigid_body, "masscenter")
    assert hasattr(rigid_body, "mass")
    assert hasattr(rigid_body, "frame")
    assert hasattr(rigid_body, "inertia")
Beispiel #3
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def test_particle_body_add_force():
    #  Body with Particle
    particle_masscenter = Point('particle_masscenter')
    particle_mass = Symbol('particle_mass')
    particle_frame = ReferenceFrame('particle_frame')
    particle_body = Body('particle_body', particle_masscenter, particle_mass,
                         particle_frame)

    a = Symbol('a')
    force_vector = a * particle_body.frame.x
    particle_body.apply_force(force_vector, particle_body.masscenter)
    assert len(particle_body.loads) == 1
    point = particle_body.masscenter.locatenew(particle_body._name + '_point0',
                                               0)
    point.set_vel(particle_body.frame, 0)
    force_point = particle_body.loads[0][0]

    frame = particle_body.frame
    assert force_point.vel(frame) == point.vel(frame)
    assert force_point.pos_from(force_point) == point.pos_from(force_point)

    assert particle_body.loads[0][1] == force_vector
Beispiel #4
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def test_default():
    body = Body('body')
    assert body.name == 'body'
    assert body.loads == []
    point = Point('body_masscenter')
    point.set_vel(body.frame, 0)
    com = body.masscenter
    frame = body.frame
    assert com.vel(frame) == point.vel(frame)
    assert body.mass == Symbol('body_mass')
    ixx, iyy, izz = symbols('body_ixx body_iyy body_izz')
    ixy, iyz, izx = symbols('body_ixy body_iyz body_izx')
    assert body.inertia == (inertia(body.frame, ixx, iyy, izz, ixy, iyz,
                                    izx), body.masscenter)
Beispiel #5
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def test_default():
    body = Body("body")
    assert body.name == "body"
    assert body.loads == []
    point = Point("body_masscenter")
    point.set_vel(body.frame, 0)
    com = body.masscenter
    frame = body.frame
    assert com.vel(frame) == point.vel(frame)
    assert body.mass == Symbol("body_mass")
    ixx, iyy, izz = symbols("body_ixx body_iyy body_izz")
    ixy, iyz, izx = symbols("body_ixy body_iyz body_izx")
    assert body.inertia == (
        inertia(body.frame, ixx, iyy, izz, ixy, iyz, izx),
        body.masscenter,
    )
Beispiel #6
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def test_particle_body():
    #  Body with Particle
    particle_masscenter = Point('particle_masscenter')
    particle_mass = Symbol('particle_mass')
    particle_frame = ReferenceFrame('particle_frame')
    particle_body = Body('particle_body', particle_masscenter, particle_mass,
                         particle_frame)
    com = particle_body.masscenter
    frame = particle_body.frame
    particle_masscenter.set_vel(particle_frame, 0)
    assert com.vel(frame) == particle_masscenter.vel(frame)
    assert com.pos_from(com) == particle_masscenter.pos_from(com)

    assert particle_body.mass == particle_mass
    assert not hasattr(particle_body, "_inertia")
    assert hasattr(particle_body, 'frame')
    assert hasattr(particle_body, 'masscenter')
    assert hasattr(particle_body, 'mass')
Beispiel #7
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def test_custom_rigid_body():
    # Body with RigidBody.
    rigidbody_masscenter = Point('rigidbody_masscenter')
    rigidbody_mass = Symbol('rigidbody_mass')
    rigidbody_frame = ReferenceFrame('rigidbody_frame')
    body_inertia = inertia(rigidbody_frame, 1, 0, 0)
    rigid_body = Body('rigidbody_body', rigidbody_masscenter, rigidbody_mass,
                      rigidbody_frame, body_inertia)
    com = rigid_body.masscenter
    frame = rigid_body.frame
    rigidbody_masscenter.set_vel(rigidbody_frame, 0)
    assert com.vel(frame) == rigidbody_masscenter.vel(frame)
    assert com.pos_from(com) == rigidbody_masscenter.pos_from(com)

    assert rigid_body.mass == rigidbody_mass
    assert rigid_body.inertia == (body_inertia, rigidbody_masscenter)

    assert hasattr(rigid_body, 'masscenter')
    assert hasattr(rigid_body, 'mass')
    assert hasattr(rigid_body, 'frame')
    assert hasattr(rigid_body, 'inertia')
Beispiel #8
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    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)
    names : str
        Names of the dynamic symbols you want to create; works the same way as
        inputs to symbols
    level : int
        Level of differentiation of the returned function; d/dt once of t,
        twice of t, etc.

    Examples
    ========

    >>> from sympy.physics.vector import dynamicsymbols
    >>> from sympy import diff, Symbol
    >>> q1 = dynamicsymbols('q1')
    >>> q1
    q1(t)
    >>> diff(q1, Symbol('t'))
    Derivative(q1(t), t)

    """
    esses = symbols(names, cls=Function)
    t = dynamicsymbols._t
    if iterable(esses):
        esses = [reduce(diff, [t] * level, e(t)) for e in esses]
        return esses
    else:
        return reduce(diff, [t] * level, esses(t))


dynamicsymbols._t = Symbol('t')
dynamicsymbols._str = '\''
Beispiel #10
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    >>> q1 = dynamicsymbols('q1')
    >>> q1
    q1(t)
    >>> q2 = dynamicsymbols('q2', real=True)
    >>> q2.is_real
    True
    >>> q3 = dynamicsymbols('q3', positive=True)
    >>> q3.is_positive
    True
    >>> q4, q5 = dynamicsymbols('q4,q5', commutative=False)
    >>> bool(q4*q5 != q5*q4)
    True
    >>> q6 = dynamicsymbols('q6', integer=True)
    >>> q6.is_integer
    True
    >>> diff(q1, Symbol('t'))
    Derivative(q1(t), t)

    """
    esses = symbols(names, cls=Function, **assumptions)
    t = dynamicsymbols._t
    if iterable(esses):
        esses = [reduce(diff, [t] * level, e(t)) for e in esses]
        return esses
    else:
        return reduce(diff, [t] * level, esses(t))


dynamicsymbols._t = Symbol('t')  # type: ignore
dynamicsymbols._str = '\''  # type: ignore
Beispiel #11
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    >>> q1 = dynamicsymbols('q1')
    >>> q1
    q1(t)
    >>> q2 = dynamicsymbols('q2', real=True)
    >>> q2.is_real
    True
    >>> q3 = dynamicsymbols('q3', positive=True)
    >>> q3.is_positive
    True
    >>> q4, q5 = dynamicsymbols('q4,q5', commutative=False)
    >>> bool(q4*q5 != q5*q4)
    True
    >>> q6 = dynamicsymbols('q6', integer=True)
    >>> q6.is_integer
    True
    >>> diff(q1, Symbol('t'))
    Derivative(q1(t), t)

    """
    esses = symbols(names, cls=Function, **assumptions)
    t = dynamicsymbols._t
    if iterable(esses):
        esses = [reduce(diff, [t] * level, e(t)) for e in esses]
        return esses
    else:
        return reduce(diff, [t] * level, esses(t))


dynamicsymbols._t = Symbol("t")  # type: ignore
dynamicsymbols._str = "'"  # type: ignore