ENH: add second order derivatives.

Co-authored-by: giovaniceotto <[email protected]>

Author: phmbressan

rocketpy/Function.py

@@ -2325,23 +2325,29 @@ def integral(self, a, b, numerical=False):
             ans, _ = integrate.quad(self, a, b, epsabs=0.001, limit=10000)
         return integrationSign * ans
 
-    def differentiate(self, x, dx=1e-6):
-        """Evaluates the derivative of a 1-D Function at x with a step size of dx.
+    def differentiate(self, x, dx=1e-6, order=1):
+        """Differentiate a Function object at a given point.
 
         Parameters
         ----------
         x : float
-            Point at which to evaluate the derivative.
+            Point at which to differentiate.
         dx : float
-            Step size to use in the derivative calculation. Default is 1e-6.
-
+            Step size to use for numerical differentiation.
+        order : int
+            Order of differentiation.
 
         Returns
         -------
-        result : float
+        ans : float
             Evaluated derivative.
         """
-        return (self.getValue(x + dx) - self.getValue(x - dx)) / (2 * dx)
+        if order == 1:
+            return (self.getValue(x + dx) - self.getValue(x - dx)) / (2 * dx)
+        elif order == 2:
+            return (
+                self.getValue(x + dx) - 2 * self.getValue(x) + self.getValue(x - dx)
+            ) / dx**2
 
     def derivativeFunction(self):
         """Returns a Function object which gives the derivative of the Function object.