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README.md

#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 some of the fundamentals of building a Trick simulation.

Here we simulate the flight of a cannon ball. We want to know the position and velocity of the cannon ball over time, given an initial position, and velocity, and 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 surface of the ground is defined as where y=0.

Solution

This problem has a closed-form solution, so that's what is used.

$v_{x0}=S\cos\theta$

$v_{y0}=S\sin\theta$

The cannon ball will impact the ground, when y(t)=0 at:

CANNON Object

Model Variable	Simulation Variable	Type	Units
,	CANNON.pos0[2]	double[2]	m
,	CANNON.vel0[2]	double[2]	m/s
$\theta$	CANNON.init_angle	double	r
	CANNON.init_speed	double	m/s
$\vec{x}$	CANNON.pos[2]	double[2]	m
$\vec{v}$	CANNON.vel[2]	double[2]	m/s