Archimedean spiral

I am trying to define the archimedean spiral: when I'm trying to define the inclination angle (incl) of the tangent vector to the orbit ( i.e: tan(incl))

I'm getting an error:

'numpy.ufunc' object does not support item assignment" and "can't assign to function call"

the same error when I want to calculate cos(incl), and sin(incl). Any suggestions and helps.

My code is:

T = 100    
N = 10000    
dt = float(T)/N 

D = 2     
DII = 10

    a = 2.     
    v = 0.23    
    omega = 0.2    
    r0 = v/omega    
    t = np.linspace(0,T,N+1)    
    r = v*t    
    theta = a + r/r0    
    theta = omega*t

    x = r * np.cos(omega*t)     
    y = r * np.sin(omega*t) 

    dxdr = np.cos(theta) - (r/r0)*np.sin(theta)    
    dydr = np.sin(theta) + (r/r0)*np.cos(theta)    
    dydx = (r0*np.sin(theta) + r*np.cos(theta))/r0*np.cos(theta) - r*np.sin(theta)

    np.tan[incl] = dydx    
    incl = np.arctan((dydx))

    ### Calculate cos(incl) ,sin(incl) :    
    np.sin[np.incl] = np.tan(np.incl)/np.sqrt(1 + np.tan(np.incl)*2)    
    np.cos[incl] = 1/np.sqrt(1 + np.tan(incl)*2)

 p1, = plt.plot(xx, yy)

i= 0 # this is the first value of the array

Bx = np.array([np.cos(i), -np.sin(i)])                    
By = np.array([np.sin(i), np.cos(i)])                     
n = 1000    
seed(2)

finalpositions = []

for number in range(0, 10):

  x = []    
  y = []    
  x.append(0)     
  y.append(0)

  for i in range(n):

      s = np.random.normal(0, 1, 2) 

      deltaX = Bx[0]*np.sqrt(2*DII*dt)*s[0] + Bx[1]*np.sqrt(2*D*dt)*s[1]          
      deltaY = By[0]*np.sqrt(2*DII*dt)*s[0] + By[1]*np.sqrt(2*D*dt)*s[1]

      x.append(x[-1] + deltaX)    
      y.append(y[-1] + deltaY)

  finalpositions.append([x[-1], y[-1]])

 p2, = plt.plot(finalpositions[:,0],finalpositions[:,1],'*')

plt.show()

Solution

The error message is correct, you are trying to assign to a function! I think you're trying to compute a value that represents the sin, cos or tan of a value, but that doesn't mean you need to assign to np.sin, etc. What you want is to calculate the value which represents the trig function, and then use the inverse trig function to get the angle:

## np.tan[incl]= dydx  ## np.tan is a function, so you cannot index it like an array, and you should not assign to it.

incl = np.arctan((dydx))  ## this is all you need to get "incl"

### Calculate cos(incl) ,sin(incl) :
## NOTE: you already have the angle you need!!  No need for a complicated formulate to compute the sin or cos!
sin_incl = np.sin(incl)
cos_incl = np.cos(incl)

EDIT: One additional comment...np is a module that contains lots of numeric methods. When you calculate incl, it is not part of np! So there is no need to reference it like np.incl. Just use incl.

EDIT2: Another problem I found is this line:

dydx = (r0*np.sin(theta) + r*np.cos(theta))/r0*np.cos(theta) - r*np.sin(theta)

To calculate dydx, you're just dividing dydr by dxdr, but that's not what your code does! You need parens around the denominator like this:

dydx = (r0*np.sin(theta) + r*np.cos(theta))/(r0*np.cos(theta) - r*np.sin(theta))