def EField(charge,point):
"""Calculate electric field caused by a charge at a point
Returns Vector
charge: Charge
Charge that cause electric field
point: Vector
Point in a 3-D space to calculate electric field
"""
E = cn.k.Value * charge.charge / veop.RelativeVector(charge.position,point).magnitude**2
vector = veop.List2Vector(E*veop.RelativeVector(point,charge.position).unitVector().numpy_array)
return vector
def CoulombsLaw(charge1,charge2):
"""Calculate electric force act on second charge applied by first charge
Returns Vector
Attributes
----------
charge1: Charge
First charge
charge2: Charge
Second Charge
"""
F = cn.k.Value * charge1.charge * charge2.charge / veop.RelativeVector(charge1.position,charge2.position).magnitude**2
vector = veop.List2Vector(F * veop.RelativeVector(charge2.position,charge1.position).unitVector().numpy_array)
return vector
def EPotential2Charge(Charge1,Charge2):
"""Calculate potential energy that created by two charges
Returns int
Attribute
---------
Charge1: Charge
First charge
Charge2: Charge
Second charge
"""
return cn.k.Value * Charge1.charge * Charge2.charge/ veop.RelativeVector(Charge1.position,Charge2.position).magnitude
def EPotential(Charge,Point):
"""Calculates electric potential energy of an charge at a point.
Returns int
Attributes
----------
Charge: Charge
A charge
Point: Vector
Point in a 3-D space
"""
return cn.k.Value * Charge.charge / veop.RelativeVector(Charge.position,Point).magnitude
def DipoleMoment(NegativeCharge,PositiveCharge):
"""Calculate the dipole moment of two charges
Returns Vector
Attribute
---------
NegativeCharge: Charge
Negative charge
PositiveCharge: Charge
Positive charge
"""
return veop.List2Vector(PositiveCharge.charge * veop.RelativeVector(PositiveCharge.position,NegativeCharge.position).numpy_array)
def Elastic(self):
"""Calculate final velocities of two object after an elastic collision
Returns Vector,Vector
Attributes
----------
Object1: Object
First object of an elactic collision
Object2: Object
Second object of an elastic collision
"""
RlV = veop.List2Vector(veop.RelativeVector(self.Object2.Velocity,self.Object1.Velocity).numpy_array)
IMom = veop.List2Vector(self.Object1.Momentum.numpy_array+self.Object2.Momentum.numpy_array)
O2fV = veop.List2Vector(IMom.numpy_array+RlV.numpy_array*self.Object1.Mass/(self.Object1.Mass+self.Object2.Mass))
O1fV = veop.List2Vector(O2fV.numpy_array-RlV.numpy_array)
return O1fV,O2fV
def GravPotential(Object,Point):
return Object.mass * veop.DotProduct(Object.Space.Gravity,veop.RelativeVector(Point,Object.Position))
def Trajectory(self,t,plot="scatter",anim=False,show_forces=False,type_of_force='net'):
"""Draws trajectory of the object between 0-t seconds
Attributes
----------
o: Object
Object
t: int
Time
"""
time_mult = 1
p = self.o.Position.components
fig = plt.figure()
plt.get_current_fig_manager().window.state('zoomed')
ax = fig.add_subplot(111, projection='3d')
ax.scatter(p[0],p[1],p[2],c='#CC0033',marker='o',s=120*2,label="Object")
ax.set_title('Trajectory of the object')
ax.set_xlabel('X axis')
ax.set_ylabel('Y axis')
ax.set_zlabel('Z axis')
if plot=="scatter":
tx = []
ty = []
tz = []
x,y,z=np.array([p[0]]),np.array([p[1]]),np.array([p[2]])
for tt in range(1,t*time_mult):
tx.append(self.o.Future("position",tt/time_mult).x)
ty.append(self.o.Future("position",tt/time_mult).y)
tz.append(self.o.Future("position",tt/time_mult).z)
if anim==True:
scat =ax.scatter(tx,ty,tz,c='black',s=50)
plt.pause(0.000001)
tx=np.array(tx)
ty=np.array(ty)
tz=np.array(tz)
self.o.Position = veop.Vector(tx,ty,tz)
spcnt = np.zeros([3,len(tx)])
space_center = veop.Vector(spcnt[0],spcnt[1],spcnt[2])
scat =ax.scatter(tx,ty,tz,c=1e-3*self.o.Mass * veop.DotProduct(self.o.Space.Gravity,veop.RelativeVector(space_center,self.o.Position)),s=60,label='Trajectory',cmap="winter",alpha=1)
x,y,z=np.append(x,tx),np.append(y,ty),np.append(z,tz)
cbar = fig.colorbar(scat)
cbar.set_label('Gravity Potential Energy (kJ)')
if show_forces == True:
force_mult = 10
f=self.o.Forces
if type_of_force=='net' or type_of_force == 'all':
x=np.append(x,tx+self.o.NetForce.x*force_mult)
y=np.append(y,ty+self.o.NetForce.y*force_mult)
z=np.append(z,tz+self.o.NetForce.z*force_mult)
ax.quiver(tx,ty,tz,self.o.NetForce.x*force_mult,self.o.NetForce.y*force_mult,self.o.NetForce.z*force_mult,colors='black',label='F_net = ({}i,{}j,{}k)'.format(self.o.NetForce.x,self.o.NetForce.y,self.o.NetForce.z))
if type_of_force=='gravity':
x=np.append(x,tx+self.o.Space.Gravity.x*force_mult)
y=np.append(y,ty+self.o.Space.Gravity.y*force_mult)
z=np.append(z,tz+self.o.Space.Gravity.z*force_mult)
ax.quiver(tx,ty,tz,self.o.Space.Gravity.x*force_mult,self.o.Space.Gravity.y*force_mult,self.o.Space.Gravity.z*force_mult,colors='red',label='Gravity = ({}i,{}j,{}k)'.format(self.o.Space.Gravity.x,self.o.Space.Gravity.y,self.o.Space.Gravity.z))
# ax.quiver(tx,ty,tz,1,1,1)
if type_of_force=='diff' or type_of_force == 'all':
colors=[]
fx,fy,fz=[],[],[]
for i in range(len(f)):
fi = f[i].components
fx.append(fi[0])
fy.append(fi[1])
fz.append(fi[2])
col = 1/len(f)
r = [0,0.5,col*i]
colors.append(r)
fx=np.array(fx)
fy=np.array(fy)
fz=np.array(fz)
for q in range(len(f)):
x=np.append(x,tx+fx[q]*force_mult)
y=np.append(y,ty+fy[q]*force_mult)
z=np.append(z,tz+fz[q]*force_mult)
fmax = max([abs(fx[q]),abs(fy[q]),abs(fz[q])])
qui_col = [ abs(fx[q])/fmax , abs(fy[q])/fmax , abs(fz[q])/fmax]
qui_col = np.array(qui_col)
qui_col = qui_col/2
ax.quiver(tx,ty,tz,fx[q]*force_mult,fy[q]*force_mult,fz[q]*force_mult,colors=qui_col,label='force {} = ({}i,{}j,{}k)'.format(q,fx[q],fy[q],fz[q]))
# print(x)
ax.set_xlim3d(min(x),max(x))
ax.set_ylim3d(min(y),max(y))
ax.set_zlim3d(min(z),max(z))
plt.legend(loc=8,ncol=5)
plt.show()
if plot=="line":
tx =[]
ty=[]
tz=[]
for tt in range(1,t*10):
# col = 1/t
# r = [0,0,1-col*tt]
# colors.append(r)
tx.append(self.o.Future("position",tt*.1).components[0])
ty.append(self.o.Future("position",tt*.1).components[1])
tz.append(self.o.Future("position",tt*.1).components[2])
ax.plot(tx,ty,tz,color="red",label='Trajectory',linewidth=5)
plt.legend()
plt.show()