Coordinate functions

In[143]:=

  r[t,c,theta0]

Out[143]=

                    2                      2
  Sqrt[Cos[c theta0]  + (t - Sin[c theta0]) ]

In[144]:=

  theta[t,c,theta0]

Out[144]=

           ArcTan[Sec[c theta0] (t - Sin[c theta0])]
  theta0 + -----------------------------------------
                               c

Now if we want to plot it, we need to do what is called "an embedding". We need to embed our paths into ordinary Euclidean space so we can plot them in Mathematica. We will use ordinary rectangular coordinates x = r Cos[theta] and y = r Sin[theta]. The embedding is this simple:

In[145]:=

  
  x[t_,c_,theta0_] := r[t,c,theta0] Cos[ theta[t,c,theta0]]

In[146]:=

  
  y[t_,c_,theta0_] := r[t,c,theta0] Sin[ theta[t,c,theta0]]

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