def __new__(self,name=None):
name = name or self.generate_name()
obj = sympy.Symbol.__new__(self,name)
pynamics.addself(obj,name)
return obj
def __init__(self,name = None):
super(Frame,self).__init__()
self.connections_R = {}
self.precomputed_R = {}
self.connections_w = {}
self.precomputed_w = {}
self.reps = {}
self.R_tree = TreeNode(self)
self.w_tree = TreeNode(self)
name = name or self.generate_name()
self.name = name
self.x = Vector()
self.y = Vector()
self.z = Vector()
self.x_sym = sympy.Symbol(name+'.x')
self.y_sym = sympy.Symbol(name+'.y')
self.z_sym = sympy.Symbol(name+'.z')
self.syms = sympy.Matrix([self.x_sym,self.y_sym,self.z_sym])
self.x.add_component(self,[1,0,0])
self.y.add_component(self,[0,1,0])
self.z.add_component(self,[0,0,1])
r = Rotation(self,self,sympy.Matrix.eye(3))
w = RotationalVelocity(self,self,sympy.Number(0)*self.x)
self.add_rotation(r)
self.add_w(w)
pynamics.addself(self,name)
def __init__(self, name, frame, pCM, mass, inertia, system):
self.name = name
self.frame = frame
self.system = system
self.pCM = pCM
self.mass = mass
self.inertia = inertia
self.vCM = self.pCM.diff_in_parts(self.system.newtonian, self.system)
self.aCM = self.vCM.diff_in_parts(self.system.newtonian, self.system)
self.gravityvector = None
self.forcegravity = None
self.wNBody = self.system.newtonian.getw_(self.frame)
self.alNBody = self.wNBody.diff_in_parts(self.system.newtonian,
self.system)
self.effectiveforce = self.mass * self.aCM
self.momentofeffectiveforce = self.inertia.dot(
self.alNBody) + self.wNBody.cross(self.inertia.dot(self.wNBody))
self.KE = .5 * mass * self.vCM.dot(self.vCM) + .5 * self.wNBody.dot(
self.inertia.dot(self.wNBody))
# self.linearmomentum = self.mass*self.vCM
# self.angularmomentum = self.inertia.dot(self.wNBody)
self.system.bodies.append(self)
self.adddynamics()
pynamics.addself(self, name)
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 __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)
pynamics.addself(obj,name)
return obj
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 __init__(self):
self.derivatives = {}
self.constants = []
self.constant_values = {}
self.forces = []
self.constraints = []
# self.momentum = []
# self.KE = sympy.Number(0)
self.bodies = []
self.particles = []
self.q = {}
self.replacements = {}
self.springs = []
self.t = sympy.Symbol('t')
self.ini = {}
self.error_tolerance = 1e-16
pynamics.addself(self, pynamics.systemname)
def __new__(cls, sys, name=None, limit=3, ii=0):
if name == None:
name = 'x{0:d}'.format(cls.ii)
cls.ii += 1
differentiables = []
for jj in range(ii, limit):
if jj == 0:
subname = name
variable = sympy.Symbol.__new__(cls, subname)
else:
subname = name + '_' + 'd' * jj
variable = sympy.Symbol.__new__(cls, subname)
sys.add_q(variable, jj)
pynamics.addself(variable, subname)
differentiables.append(variable)
for a, a_d in zip(differentiables[:-1], differentiables[1:]):
sys.add_derivative(a, a_d)
return differentiables
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)
pynamics.addself(self, self.name)
self.effectiveforces = []
def __init__(self,name = None):
super(Frame,self).__init__()
self.connections = {}
self.precomputed = {}
self.reps = {}
if name==None:
name=Name.frame()
self.name = name
self.x = Vector()
self.y = Vector()
self.z = Vector()
self.x_sym = sympy.Symbol(name+'.x')
self.y_sym = sympy.Symbol(name+'.y')
self.z_sym = sympy.Symbol(name+'.z')
self.syms = sympy.Matrix([self.x_sym,self.y_sym,self.z_sym])
self.x.add_component(self,[1,0,0])
self.y.add_component(self,[0,1,0])
self.z.add_component(self,[0,0,1])
self.add_rotation(Rotation(self,self,sympy.Matrix.eye(3),sympy.Number(0)*self.x))
pynamics.addself(self,name)
def __new__(self, name, value, system):
obj = sympy.Symbol.__new__(self, name)
obj.value = value
system.add_constant(obj, value)
pynamics.addself(obj, name)
return obj
def __new__(self, name):
obj = sympy.Symbol.__new__(self, name)
pynamics.addself(obj, name)
return obj