fix: improve docs and comments

mathpad/mech.py

@@ -1,4 +1,3 @@
-from typing import Type, cast
 from mathpad import *
 
 
@@ -15,10 +14,10 @@ def kinetic_energy(*, m: X[Mass], v: X[Velocity]) -> Energy:
         Kinetic energy of the particle in joules
 
     Example:
-        >>> kinetic_energy(m=1 * kg, v=2 * m/s)
-        2 joules
         >>> kinetic_energy(m="m" * kg, v="v" * m/s)
         0.5*mv**2 joules
+        >>> kinetic_energy(m=1 * kg, v=2 * m/s)
+        2 joules
 
     """
     return (m * v ** 2 / 2).in_units(joules)  # type: ignore
@@ -46,11 +45,10 @@ def euler_lagrange(
     Euler-Lagrange equation for a system of particles.
 
     Arguments:
-        sum_KE: sum of kinetic energies of particles
-        sum_PE: sum of potential energies of particles
-        sum_NCF: sum of net contact forces on particles
+        KE: sum of kinetic energies of particles
+        PE: sum of potential energies of particles
+        NCF: sum of net contact forces on particles
         var: variable you are interested in finding the dynamics for
-    
     """
     L = KE - PE
     return diff(diff(L, wrt=diff(var)), wrt=t) - diff(L, wrt=var) == NCF # type: ignore
@@ -62,7 +60,7 @@ def impulse_momentum(
     m: X[Mass],  # mass
     v1: X[Velocity],  # initial velocity
     F: X[Force],  # impulse force required
-    t: X[Time],  # impulse duration in seconds
+    t: X[Time],  # impulse duration
     v2: X[Velocity],  # final velocity
 ) -> Equation:
     "The force required during an instant to change an object's velocity"

mathpad/simulate_dynamic_system.py

@@ -190,7 +190,7 @@ def simulate_dynamic_system(
         ]
 
         # outputs are highest of input derviatives plus recorded data
-        # ie [dddx, record[0], record[1]]
+        # ie [ddx, ddy, record[0], record[1]]
         lambdified = lambdify([x_axis.expr, inputs], solution_vec, 'numpy')
 
         data = []
@@ -285,7 +285,7 @@ def step(x: float, state: np.ndarray):
                         "yanchor": "top",
                     },
                 },
-            ).show("svg" if plot_static else None)
+            ).show("svg" if plot_static else None) # type: ignore
 
         all_data.extend(data)