SmtC: Show me the Code!

< Evolute | 2nd Order | Determinant >

Hat Vector: Rotate 90 degrees.
[; \underline{a}= \left( \begin{array}{c} a_1\\a_2 \end{array} \right): \qquad \qquad \underline{ \widehat{a} } := \left( \begin{array}{c} -a_2\\a_1 \end{array} \right) ;]
Acceleration Vector: [; \underline{a}(t)=\underline{r}''(t)= \left( \begin{array}{c} x''(t)\\y''(t) \end{array} \right) ;]
Taylor's Formula 2nd Order: [; \underline{r}(t)= \underline{r}(t_0) +(t-t_0) \underline{r}'(t_0) +1/2 (t-t_0)^2 \underline{r}''(t+0) +(t-t_0)^2 \underline{\epsilon}(t) ;]
Aproximation by Circle: Quadratic Fit
Newton's II Law: [; m \cdot \underline{a}(t)=\underline{F}_{~ex}(t) ;]

Python Listing: Derivative2.py.

    def dR2(t):
       return (
           self.dR(t+self.eps)-self.dR(t-self.eps)
       )*self.eps2inv

    d2Rs=[]
    ##!
    ##! Calculate and store 2nd derivatives.
    ##!
    
    def Calc_d2Rs(self,ts=[]):
        ts=self.Get_ts(ts)
        self.dR=[]
        for i in range( len(ts )):
            self.dR[i]=self.dR2(ts[i])
            
        return self.d2Rs

< Evolute | 2nd Order | Determinant >