Create README for SIM_cannon_analytic

trick_sims/SIM_cannon_analytic/README.md

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+#SIM\_cannon\_analytic
+---
+This is first of eight Trick-based simulations that one builds in the Trick
+Tutorial (Section 3). It's purpose is to introduce the fundamentals of building
+a Trick simulation.
+
+Here we simulate the flight of a cannon ball, given an initial position, and
+velocity subject to the following assumptions and limitations:
+
+* The **only** force acting on the cannon ball is gravity.
+* The acceleration of gravity (g) is constant and equal to -9.81 meters per
+  second squared.
+* The ground is flat, and here, defined as where y=0.
+
+![X(t) = Vx * t + X0](images/CannonInit.png)
+
+--
+### Approach
+
+Since this problem has a closed-form solution, that's what we use :
+
+![X(t) = Vx * t + X0](images/solution_x.png)
+
+![Y(t) = (1/2)gt^2 + Vy * t + Y0](images/solution_y.png)
+
+The time when the cannon ball impacts the ground is:
+
+![](images/time_of_impact.png)
+
+--
+### Inputs
+Variable               | Type           | Units
+-----------------------|----------------|-------
+dyn.cannon.pos0        | double[2]      | m
+dyn.cannon.init\_angle | double         | r
+dyn.cannon.init\_speed | double         | m/s
+
+The initial velocity is :
+
+![Vx = speed * cos(angle)](images/initial_vel_x.png),
+![Vy = speed * sin(angle)](images/initial_vel_y.png)
+
+--
+### Outputs
+Variable               | Type           | Units
+-----------------------|----------------|--------
+dyn.cannon.pos         | double[2]      | m
+dyn.cannon.vel         | double[2]      | m/s