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#Calculus for the WP@ELAB training 
 
 
* [The presentation](Presentation/main.pdf) ([source](Presentation/))
* [Resources](rsrcs/)


## Examples

### 1D 0th order ODE problem: Constant force

* [1D Dynamics with constant force](http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/examples/Spreadsheets/0stO_ConstForce/)


### 1D 1st order ODE problem: Friction force ($v$ dependence)

* [1D Dynamics with friction force](http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/examples/Spreadsheets/1stO_Friction/)



### 1D 2nd order ODE problem: Free fall (full dynamics)

* Spreadsheets
    * [1D free fall example (basic version)](http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/examples/Spreadsheets/1D_FreeFall_Basic/)
    * [1D free fall example (version with named parameters)](http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/examples/Spreadsheets/1D_FreeFall_NamedCells/)
* Processing ([see processing.org](https://processing.org/), [try it](https://editor.p5js.org/))
    * [1D free fall](https://editor.p5js.org/vojtech.svob/sketches/p_VGqDX5)
* Python @ JupyterNotebook ([see jupyter.org](https://jupyter.org/))
    * [1D free fall](http://buon.fjfi.cvut.cz/raws/CTU4WP@ELAB/examples/PythonJupyterNotebook/1D_Freefall_Num/model.html)
    
    
### 1D 2nd order ODE problem: Pendulum (full dynamics)
* Spreadsheets
    * [Pendulum (basic version)](http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/examples/Spreadsheets/1D_Pendulum_Basic/)
    * [Pendulum with friction](http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/examples/Spreadsheets/1D_Pendulum_Friction/)
    * [Pendulum with friction - phase space](http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/examples/Spreadsheets/1D_Pendulum_Friction_PhaseSpace/)
    * [Pendulum - energy conservation analysis](http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/examples/Spreadsheets/1D_Pendulum_EnergyConservation/)
    * [Pendulum - small angle approximation analysis](http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/examples/Spreadsheets/1D_Pendulum_SmallAngleApprox/)
* Processing ([see processing.org](https://processing.org/), [try it](https://editor.p5js.org/))
    * [pendulum (basic version)](https://editor.p5js.org/vojtech.svob/sketches/vTEaAkgs)
    * [pendulum ("advanced" version)](https://editor.p5js.org/vojtech.svob/sketches/g7eW0UY-)
    * [pendulum with friction](https://editor.p5js.org/vojtech.svob/sketches/qHurFykr)
    * [two pendulums](https://editor.p5js.org/vojtech.svob/sketches/vXqfkyzU) ([wiki/Gravity_of_Earth](https://en.wikipedia.org/wiki/Gravity_of_Earth): sea-level gravity increases from about 9.780 m/s2 at the Equator to about 9.832 m/s2 at the poles)
    
## Simulation and experiment

### Prague

* [Pendulum in Prague (Charles university)](http://kdt-40.karlov.mff.cuni.cz/)
* [Processing](https://editor.p5js.org/vojtech.svob/sketches/qes6mq_o)

### Bogota

* [Processing](https://editor.p5js.org/vojtech.svob/sketches/ni4EgKh-)

## 2D problem: Horizontal Launch

* [Spreadsheet approach](http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/examples/Spreadsheets/2D_HorizontalLaunch_Basic/)
* [Processing approach](https://editor.p5js.org/vojtech.svob/sketches/3O2OUtpW)



## Relevant info

* Gravitational constants at important places [from Local Acceleration of Gravity@Wolfram](https://www.wolframalpha.com/widgets/view.jsp?id=e856809e0d522d3153e2e7e8ec263bf2) [m/s**2]
    * Barcelona 9.799 
    * Bogota 9.776 
    * Lisbon 9.814 
    * Marseille 9.822 
    * Panama 9.778  
    * Prague 9.834 
    * Rio de Janeiro 9.791 
    * Santiago de Chile 9.806 
    
    
    
## References

* [Daniel A. Russell: Oscillation of a Simple Pendulum (accessed March 2, 2020).](https://www.acs.psu.edu/drussell/Demos/Pendulum/Pendulum.html)
* [Wikipedia contributors, "Pendulum (mathematics)," Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/w/index.php?title=Pendulum_(mathematics)&oldid=942104313 (accessed March 2, 2020).](https://en.wikipedia.org/w/index.php?title=Pendulum_(mathematics)&oldid=942104313)
* [Local Acceleration of Gravity@Wolfram (accessed March 2, 2020).](https://www.wolframalpha.com/widgets/view.jsp?id=e856809e0d522d3153e2e7e8ec263bf2)




## Authors

* [Vojtech Svoboda (Czech Technical University in Prague)](mailto:vojtech.svoboda@fjfi.cvut.cz )
* [Pavel Kuriscak (Charles University in Prague)](mailto:pavel.kuriscak@gmail.com)
* [Frantisek Lustig (Charles University in Prague)](mailto:fl@plk.mff.cuni.cz)

<img src="qrcode.png" width=30%>
[http://buon.fjfi.cvut.cz/wp](http://buon.fjfi.cvut.cz/wp) 

<hr>
[Any comments, suggestions, ideas highly appreciated. Thanks in advance. Authors.](mailto:vojtech.svoboda@fjfi.cvut.cz )