trick/trick_sims/Cannon/SIM_cannon_numeric/README.md

# SIM\_cannon\_numeric

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This is the second in a series example cannon ball simulations that one builds in the Trick Tutorial (Sections 9, 10). It's purpose is to introduce Trick supported numerical methods. 

Rather than using the analytic solutions of SIM\_cannon\_analytic, this simulation uses Trick's numerical integration, and root-finding methods to:

* Determine the cannon ball state (velocity, position) at each time step, and
* Determine when and where the cannon ball impacts the ground.

The simulation is otherwise the same as SIM\_cannon\_analytic.

![CannonPicture](images/CannonInit.png)

## Parameterization
Same as in SIM\_cannon\_analytic.

## Initialization
Same as in SIM\_cannon\_analytic.

## State Propagation

This Trick simulation calculates the cannonball state by numerical integration.
Acceleration is calculated in the "derivative" job **cannon\_deriv**. It is then
used in "integration" job **cannon\_integ** to calculate the cannonball's velocity and
position, using the Trick **integrate** function.
 
## When and Where the Ball Impacts the Ground
The time and position of impact is determined by the "dynamic\_event" event job
**cannon\_impact**, using the Trick **regula_falsi** function.