def set_pos(self, otherpoint, value):
"""Used to set the position of this point w.r.t. another point.
Parameters
==========
value : Vector
The vector which defines the location of this point
point : Point
The other point which this point's location is defined relative to
Examples
========
>>> from sympy.physics.mechanics import Point, ReferenceFrame
>>> N = ReferenceFrame('N')
>>> p1 = Point('p1')
>>> p2 = Point('p2')
>>> p1.set_pos(p2, 10 * N.x)
>>> p1.pos_from(p2)
10*N.x
"""
value = _check_vector(value)
self._check_point(otherpoint)
self._pos_dict.update({otherpoint: value})
otherpoint._pos_dict.update({self: -value})
def set_vel(self, frame, value):
"""Sets the velocity Vector of this Point in a ReferenceFrame.
Parameters
==========
value : Vector
The vector value of this point's velocity in the frame
frame : ReferenceFrame
The frame in which this point's velocity is defined
Examples
========
>>> from sympy.physics.mechanics import Point, ReferenceFrame
>>> N = ReferenceFrame('N')
>>> p1 = Point('p1')
>>> p1.set_vel(N, 10 * N.x)
>>> p1.vel(N)
10*N.x
"""
value = _check_vector(value)
_check_frame(frame)
self._vel_dict.update({frame: value})
def locatenew(self, name, value):
"""Creates a new point with a position defined from this point.
Parameters
==========
name : str
The name for the new point
value : Vector
The position of the new point relative to this point
Examples
========
>>> from sympy.physics.mechanics import ReferenceFrame, Point
>>> N = ReferenceFrame('N')
>>> P1 = Point('P1')
>>> P2 = P1.locatenew('P2', 10 * N.x)
"""
if not isinstance(name, str):
raise TypeError('Must supply a valid name')
value = _check_vector(value)
p = Point(name)
p.set_pos(self, value)
self.set_pos(p, -value)
return p
def set_acc(self, frame, value):
"""Used to set the acceleration of this Point in a ReferenceFrame.
Parameters
==========
value : Vector
The vector value of this point's acceleration in the frame
frame : ReferenceFrame
The frame in which this point's acceleration is defined
Examples
========
>>> from sympy.physics.mechanics import Point, ReferenceFrame
>>> N = ReferenceFrame('N')
>>> p1 = Point('p1')
>>> p1.set_acc(N, 10 * N.x)
>>> p1.acc(N)
10*N.x
"""
value = _check_vector(value)
_check_frame(frame)
self._acc_dict.update({frame: value})
def set_pos(self, otherpoint, value):
"""Used to set the position of this point w.r.t. another point.
Parameters
==========
value : Vector
The vector which defines the location of this point
point : Point
The other point which this point's location is defined relative to
Examples
========
>>> from sympy.physics.mechanics import Point, ReferenceFrame
>>> N = ReferenceFrame('N')
>>> p1 = Point('p1')
>>> p2 = Point('p2')
>>> p1.set_pos(p2, 10 * N.x)
>>> p1.pos_from(p2)
10*N.x
"""
value = _check_vector(value)
self._check_point(otherpoint)
self._pos_dict.update({otherpoint: value})
otherpoint._pos_dict.update({self: -value})
def set_vel(self, frame, value):
"""Sets the velocity Vector of this Point in a ReferenceFrame.
Parameters
==========
value : Vector
The vector value of this point's velocity in the frame
frame : ReferenceFrame
The frame in which this point's velocity is defined
Examples
========
>>> from sympy.physics.mechanics import Point, ReferenceFrame
>>> N = ReferenceFrame('N')
>>> p1 = Point('p1')
>>> p1.set_vel(N, 10 * N.x)
>>> p1.vel(N)
10*N.x
"""
value = _check_vector(value)
_check_frame(frame)
self._vel_dict.update({frame: value})
def set_acc(self, frame, value):
"""Used to set the acceleration of this Point in a ReferenceFrame.
Parameters
==========
value : Vector
The vector value of this point's acceleration in the frame
frame : ReferenceFrame
The frame in which this point's acceleration is defined
Examples
========
>>> from sympy.physics.mechanics import Point, ReferenceFrame
>>> N = ReferenceFrame('N')
>>> p1 = Point('p1')
>>> p1.set_acc(N, 10 * N.x)
>>> p1.acc(N)
10*N.x
"""
value = _check_vector(value)
_check_frame(frame)
self._acc_dict.update({frame: value})
def locatenew(self, name, value):
"""Creates a new point with a position defined from this point.
Parameters
==========
name : str
The name for the new point
value : Vector
The position of the new point relative to this point
Examples
========
>>> from sympy.physics.mechanics import ReferenceFrame, Point
>>> N = ReferenceFrame('N')
>>> P1 = Point('P1')
>>> P2 = P1.locatenew('P2', 10 * N.x)
"""
if not isinstance(name, str):
raise TypeError('Must supply a valid name')
value = _check_vector(value)
p = Point(name)
p.set_pos(self, value)
self.set_pos(p, -value)
return p
def get_motion_params(frame, **kwargs):
"""
Returns the three motion parameters - (acceleration, velocity, and
position) as vectorial functions of time in the given frame.
If a higher order differential function is provided, the lower order
functions are used as boundary conditions. For example, given the
acceleration, the velocity and position parameters are taken as
boundary conditions.
The values of time at which the boundary conditions are specified
are taken from timevalue1(for position boundary condition) and
timevalue2(for velocity boundary condition).
If any of the boundary conditions are not provided, they are taken
to be zero by default (zero vectors, in case of vectorial inputs). If
the boundary conditions are also functions of time, they are converted
to constants by substituting the time values in the dynamicsymbols._t
time Symbol.
This function can also be used for calculating rotational motion
parameters. Have a look at the Parameters and Examples for more clarity.
Parameters
==========
frame : ReferenceFrame
The frame to express the motion parameters in
acceleration : Vector
Acceleration of the object/frame as a function of time
velocity : Vector
Velocity as function of time or as boundary condition
of velocity at time = timevalue1
position : Vector
Velocity as function of time or as boundary condition
of velocity at time = timevalue1
timevalue1 : sympyfiable
Value of time for position boundary condition
timevalue2 : sympyfiable
Value of time for velocity boundary condition
Examples
========
>>> from sympy.physics.mechanics import ReferenceFrame, get_motion_params, dynamicsymbols
>>> from sympy import symbols
>>> R = ReferenceFrame('R')
>>> v1, v2, v3 = dynamicsymbols('v1 v2 v3')
>>> v = v1*R.x + v2*R.y + v3*R.z
>>> get_motion_params(R, position = v)
(v1''*R.x + v2''*R.y + v3''*R.z, v1'*R.x + v2'*R.y + v3'*R.z, v1*R.x + v2*R.y + v3*R.z)
>>> a, b, c = symbols('a b c')
>>> v = a*R.x + b*R.y + c*R.z
>>> get_motion_params(R, velocity = v)
(0, a*R.x + b*R.y + c*R.z, a*t*R.x + b*t*R.y + c*t*R.z)
>>> parameters = get_motion_params(R, acceleration = v)
>>> parameters[1]
a*t*R.x + b*t*R.y + c*t*R.z
>>> parameters[2]
a*t**2/2*R.x + b*t**2/2*R.y + c*t**2/2*R.z
"""
##Helper functions
def _process_vector_differential(vectdiff, condition, \
variable, ordinate, frame):
"""
Helper function for get_motion methods. Finds derivative of vectdiff wrt
variable, and its integral using the specified boundary condition at
value of variable = ordinate.
Returns a tuple of - (derivative, function and integral) wrt vectdiff
"""
#Make sure boundary condition is independent of 'variable'
if condition != 0:
condition = frame.express(condition)
#Special case of vectdiff == 0
if vectdiff == Vector(0):
return (0, 0, condition)
#Express vectdiff completely in condition's frame to give vectdiff1
vectdiff1 = frame.express(vectdiff)
#Find derivative of vectdiff
vectdiff2 = frame.dt(vectdiff)
#Integrate and use boundary condition
vectdiff0 = Vector(0)
lims = (variable, ordinate, variable)
for dim in frame:
function1 = vectdiff1.dot(dim)
abscissa = dim.dot(condition).subs({variable: ordinate})
# Indefinite integral of 'function1' wrt 'variable', using
# the given initial condition (ordinate, abscissa).
vectdiff0 += (integrate(function1, lims) + abscissa) * dim
#Return tuple
return (vectdiff2, vectdiff, vectdiff0)
##Function body
_check_frame(frame)
#Decide mode of operation based on user's input
if 'acceleration' in kwargs:
mode = 2
elif 'velocity' in kwargs:
mode = 1
else:
mode = 0
#All the possible parameters in kwargs
#Not all are required for every case
#If not specified, set to default values(may or may not be used in
#calculations)
conditions = [
'acceleration', 'velocity', 'position', 'timevalue', 'timevalue1',
'timevalue2'
]
for i, x in enumerate(conditions):
if x not in kwargs:
if i < 3:
kwargs[x] = Vector(0)
else:
kwargs[x] = S(0)
elif i < 3:
_check_vector(kwargs[x])
else:
kwargs[x] = sympify(kwargs[x])
if mode == 2:
vel = _process_vector_differential(kwargs['acceleration'],
kwargs['velocity'],
dynamicsymbols._t,
kwargs['timevalue2'], frame)[2]
pos = _process_vector_differential(vel, kwargs['position'],
dynamicsymbols._t,
kwargs['timevalue1'], frame)[2]
return (kwargs['acceleration'], vel, pos)
elif mode == 1:
return _process_vector_differential(kwargs['velocity'],
kwargs['position'],
dynamicsymbols._t,
kwargs['timevalue1'], frame)
else:
vel = frame.dt(kwargs['position'])
acc = frame.dt(vel)
return (acc, vel, kwargs['position'])
def _set_gravity_vector(self, vec):
_check_vector(vec)
self._gravity_vector = vec
self._gravity_vector_updated.fire()
def get_motion_params(frame, **kwargs):
"""
Returns the three motion parameters - (acceleration, velocity, and
position) as vectorial functions of time in the given frame.
If a higher order differential function is provided, the lower order
functions are used as boundary conditions. For example, given the
acceleration, the velocity and position parameters are taken as
boundary conditions.
The values of time at which the boundary conditions are specified
are taken from timevalue1(for position boundary condition) and
timevalue2(for velocity boundary condition).
If any of the boundary conditions are not provided, they are taken
to be zero by default (zero vectors, in case of vectorial inputs). If
the boundary conditions are also functions of time, they are converted
to constants by substituting the time values in the dynamicsymbols._t
time Symbol.
This function can also be used for calculating rotational motion
parameters. Have a look at the Parameters and Examples for more clarity.
Parameters
==========
frame : ReferenceFrame
The frame to express the motion parameters in
acceleration : Vector
Acceleration of the object/frame as a function of time
velocity : Vector
Velocity as function of time or as boundary condition
of velocity at time = timevalue1
position : Vector
Velocity as function of time or as boundary condition
of velocity at time = timevalue1
timevalue1 : sympyfiable
Value of time for position boundary condition
timevalue2 : sympyfiable
Value of time for velocity boundary condition
Examples
========
>>> from sympy.physics.mechanics import ReferenceFrame, get_motion_params, dynamicsymbols
>>> from sympy import symbols
>>> R = ReferenceFrame('R')
>>> v1, v2, v3 = dynamicsymbols('v1 v2 v3')
>>> v = v1*R.x + v2*R.y + v3*R.z
>>> get_motion_params(R, position = v)
(v1''*R.x + v2''*R.y + v3''*R.z, v1'*R.x + v2'*R.y + v3'*R.z, v1*R.x + v2*R.y + v3*R.z)
>>> a, b, c = symbols('a b c')
>>> v = a*R.x + b*R.y + c*R.z
>>> get_motion_params(R, velocity = v)
(0, a*R.x + b*R.y + c*R.z, a*t*R.x + b*t*R.y + c*t*R.z)
>>> parameters = get_motion_params(R, acceleration = v)
>>> parameters[1]
a*t*R.x + b*t*R.y + c*t*R.z
>>> parameters[2]
a*t**2/2*R.x + b*t**2/2*R.y + c*t**2/2*R.z
"""
##Helper functions
def _process_vector_differential(vectdiff, condition, \
variable, ordinate, frame):
"""
Helper function for get_motion methods. Finds derivative of vectdiff wrt
variable, and its integral using the specified boundary condition at
value of variable = ordinate.
Returns a tuple of - (derivative, function and integral) wrt vectdiff
"""
#Make sure boundary condition is independent of 'variable'
if condition != 0:
condition = frame.express(condition)
#Special case of vectdiff == 0
if vectdiff == Vector(0):
return (0, 0, condition)
#Express vectdiff completely in condition's frame to give vectdiff1
vectdiff1 = frame.express(vectdiff)
#Find derivative of vectdiff
vectdiff2 = frame.dt(vectdiff)
#Integrate and use boundary condition
vectdiff0 = Vector(0)
lims = (variable, ordinate, variable)
for dim in frame:
function1 = vectdiff1.dot(dim)
abscissa = dim.dot(condition).subs({variable:ordinate})
# Indefinite integral of 'function1' wrt 'variable', using
# the given initial condition (ordinate, abscissa).
vectdiff0 += (integrate(function1, lims) + abscissa)*dim
#Return tuple
return (vectdiff2, vectdiff, vectdiff0)
##Function body
_check_frame(frame)
#Decide mode of operation based on user's input
if 'acceleration' in kwargs:
mode = 2
elif 'velocity' in kwargs:
mode = 1
else:
mode = 0
#All the possible parameters in kwargs
#Not all are required for every case
#If not specified, set to default values(may or may not be used in
#calculations)
conditions = ['acceleration', 'velocity', 'position',
'timevalue', 'timevalue1', 'timevalue2']
for i, x in enumerate(conditions):
if x not in kwargs:
if i < 3:
kwargs[x] = Vector(0)
else:
kwargs[x] = S(0)
elif i < 3:
_check_vector(kwargs[x])
else:
kwargs[x] = sympify(kwargs[x])
if mode == 2:
vel = _process_vector_differential(kwargs['acceleration'],
kwargs['velocity'],
dynamicsymbols._t,
kwargs['timevalue2'], frame)[2]
pos = _process_vector_differential(vel, kwargs['position'],
dynamicsymbols._t,
kwargs['timevalue1'], frame)[2]
return (kwargs['acceleration'], vel, pos)
elif mode == 1:
return _process_vector_differential(kwargs['velocity'],
kwargs['position'],
dynamicsymbols._t,
kwargs['timevalue1'], frame)
else:
vel = frame.dt(kwargs['position'])
acc = frame.dt(vel)
return (acc, vel, kwargs['position'])
def _set_gravity_vector(self, vec):
_check_vector(vec)
self._gravity_vector = vec
self._gravity_vector_updated.fire()
