def diff_simple(self, frame, sys=None):
sys = sys or pynamics.get_system()
v = self.express(frame).components[frame]
dv = sys.derivative(v)
newvec = Vector({frame: dv})
newvec.clean()
return newvec
def __init__(self,
name,
frame,
pCM,
mass,
inertia_CM,
system=None,
about_point=None,
about_point_d=None,
about_point_dd=None,
vCM=None,
aCM=None,
wNBody=None,
alNBody=None,
inertia_about_point=None):
system = system or pynamics.get_system()
name = name or self.generate_name()
self.name = name
self.frame = frame
self.system = system
self.pCM = pCM
self.mass = mass
self.inertia_CM = inertia_CM
self.vCM = vCM or self.pCM.time_derivative(self.system.newtonian,
self.system)
self.aCM = aCM or self.vCM.time_derivative(self.system.newtonian,
self.system)
if about_point is None:
self.about_point = pCM
self.about_point_d = self.vCM
self.about_point_dd = self.aCM
else:
self.about_point = about_point
self.about_point_d = about_point_d or self.about_point.time_derivative(
self.system.newtonian, self.system)
self.about_point_dd = about_point_dd or self.about_point_d.time_derivative(
self.system.newtonian, self.system)
self.inertia_about_point = inertia_about_point or pynamics.inertia.shift_from_cm(
self.inertia_CM, self.pCM, self.about_point, self.mass, self.frame)
self.gravityvector = None
self.forcegravity = None
self.wNBody = wNBody or self.system.newtonian.getw_(self.frame)
self.alNBody = alNBody or self.wNBody.time_derivative(
self.system.newtonian, self.system)
# self.linearmomentum = self.mass*self.vCM
# self.angularmomentum = self.inertia.dot(self.wNBody)
self.system.bodies.append(self)
pynamics.addself(self, name)
self.effectiveforces = []
def __init__(self,y_exp, system=None, constant_values = None,state_variables = None):
import sympy
system = system or pynamics.get_system()
state_variables = state_variables or system.get_state_variables()
constant_values = constant_values or system.constant_values
self.y_expression = sympy.Matrix(y_exp)
cons_s = list(constant_values.keys())
self.cons_v = [constant_values[key] for key in cons_s]
self.fy_expression = sympy.lambdify(state_variables+cons_s+[system.t],self.y_expression)
def w_from_fixed_axis(axis, q, frame, sys=None):
sys = sys or pynamics.get_system()
axis = sympy.Matrix(axis)
l_2 = axis.dot(axis)
axis = axis / (l_2**.5)
w = sys.derivative(q)
w_ = w * Vector({frame: axis})
return w_
def rotate_fixed_axis(self,fromframe,axis,q,system = None):
system = system or pynamics.get_system()
rotation = Rotation.build_fixed_axis(fromframe,self,axis,q,system)
rotational_velocity = RotationalVelocity.build_fixed_axis(fromframe,self,axis,q,system)
self.add_rotation(rotation)
self.add_w(rotational_velocity)
fromframe.add_rotation(rotation)
fromframe.add_w(rotational_velocity)
fromframe.R_tree.add_branch(self.R_tree)
fromframe.w_tree.add_branch(self.w_tree)
def time_derivative(self, reference_frame=None, system=None):
system = system or pynamics.get_system()
reference_frame = reference_frame or system.newtonian
result = Vector()
for frame, vector in self.components.items():
result += Vector({frame: system.derivative(vector)})
v1 = Vector({frame: vector})
w_ = reference_frame.getw_(frame).express(frame)
result += w_.cross(v1, frame='mid')
result.clean()
return result
def __new__(self, value=None, name=None, system=None):
name = name or self.generate_name()
system = system or pynamics.get_system()
obj = sympy.Symbol.__new__(self, name)
# obj.value = value
system.add_constant(obj)
if value is not None:
system.add_constant_value(obj, value)
return obj
def __init__(self,
y_exp,
system=None,
constant_values=None,
state_variables=None,
dot=None):
system = system or pynamics.get_system()
dot = dot or [system.newtonian.x, system.newtonian.y]
y_exp = [
item for item2 in y_exp
for item in [item2.dot(dotitem) for dotitem in dot]
]
Output.__init__(self, y_exp, system, constant_values, state_variables)
def __new__(cls,name=None,system = None,limit = 3,ii=0,ini = None):
system = system or pynamics.get_system()
name = name or cls.generate_name()
output = []
differentiables = []
for kk,jj in enumerate(range(ii,limit)):
if kk==0:
subname = name
variable = sympy.Symbol.__new__(cls,subname)
else:
subname = name+'_'+'d'*kk
# if jj==limit-1:
# variable = Variable(subname)
# else:
# variable = sympy.Symbol.__new__(cls,subname)
variable = sympy.Symbol.__new__(cls,subname)
pynamics.addself(variable,subname)
output.append(variable)
# if jj!=limit-1:
# differentiables.append(variable)
# system.add_q(variable,jj)
differentiables.append(variable)
system.add_q(variable,jj)
# for item in differentiables:
# system.set_derivative(item,None)
for kk,(a,a_d) in enumerate(zip(output[:-1],output[1:])):
system.set_derivative(a,a_d)
if ini is not None:
system.set_ini(a,ini[kk])
if len(output)==1:
return output[0]
else:
return output
def __new__(cls,
name=None,
system=None,
limit=3,
ii=0,
ini=None,
output_full=True):
system = system or pynamics.get_system()
name = name or cls.generate_name()
output = []
for kk, jj in enumerate(range(ii, limit)):
if kk == 0:
subname = name
variable = sympy.Symbol.__new__(cls, subname)
else:
subname = name + '_' + 'd' * kk
# if jj==limit-1:
# variable = Variable(subname)
# else:
# variable = sympy.Symbol.__new__(cls,subname)
variable = sympy.Symbol.__new__(cls, subname)
output.append(variable)
system.add_q(variable, jj)
for item in output:
item.set_derivative(sympy.Number(0))
for kk, (a, a_d) in enumerate(zip(output[:-1], output[1:])):
system.set_derivative(a, a_d)
a.set_derivative(a_d)
if ini is not None:
system.set_ini(a, ini[kk])
if output_full:
if len(output) == 1:
return output[0]
else:
return output
else:
return output[0]
def build_fixed_axis(axis, q, frame, sys=None):
sys = sys or pynamics.get_system()
axis = sympy.Matrix(axis)
l_2 = axis.dot(axis)
axis = axis / (l_2**.5)
e0 = axis[0]
e1 = axis[1]
e2 = axis[2]
c = axis * axis.T
a = (sympy.Matrix.eye(3) - c) * cos(q)
b = sympy.Matrix([[0, -e2, e1], [e2, 0, -e0], [-e1, e0, 0]]) * sin(q)
R = a + b + c
R = R.T
return R, axis
def __init__(self, pCM, mass, name=None, system=None, vCM=None, aCM=None):
system = system or pynamics.get_system()
name = name or self.generate_name()
self.name = name
self.pCM = pCM
self.mass = mass
self.system = system
self.vCM = vCM or self.pCM.time_derivative(self.system.newtonian,
self.system)
self.aCM = aCM or self.vCM.time_derivative(self.system.newtonian,
self.system)
self.gravityvector = None
self.forcegravity = None
self.system.particles.append(self)
self.effectiveforces = []
