trick/trick_sims/Cannon/SIM_cannon_analytic

SIM_cannon_analytic

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This is first of eight Trick-based simulations that one builds in the Trick Tutorial (Section 4). 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.

Parameterization

The following parameters are given default values in a "default_data" job called cannon_default_data. Their values can be changed in the input.py file.

Name	Sim Variable	Type	Units	Symbol	default
Barrel Angle	dyn.cannon.init_angle	double	radians		30*(π/180)
Speed	dyn.cannon.init_speed	double	m/s		50.0
Gravity	dyn.cannon.g	double	m/s		9.81
Initial Position	dyn.cannon.pos0	double[2]	m

Initialization

The initial velocity is calculated in an "initialization" job.

Name	Sim Variable	Type	Units	Calculation
Initial Velocity	dyn.cannon.vel0	double[2]	m/s

State Propagation

For each time-step, the following are calculated in a "scheduled" job. Though acceleration is constant in this simulation, it usually isn't for "F=ma" type simulations.

Name	Sim Variable	Type	Units	Calculation
Acceleration	dyn.cannon.acc	double[2]	m/s²
Velocity(t)	dyn.cannon.vel	double[2]	m/s
Position(t)	dyn.cannon.pos	double[2]	m

Calculating When the Ball Impacts the Ground.

The cannon ball will impact the ground, when y-element of the position vector is zero.

Name	Sim Variable	Type	Units	Calculation
Time of Impact	dyn.cannon.impactTime	double	s