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# Calculus for the WP@ELAB training
[mail to main author Vojtech Svoboda](mailto:vojtech.svoboda@fjfi.cvut.cz )
* [The presentation](Presentation/main.pdf) ([latex source](Presentation/))
* [Resources](rsrcs/)
* [Examples](Presentation/examples/)
* [all in zip](http://buon.fjfi.cvut.cz/raws/CTU4WP@ELAB/CTU4WP.zip)
## Examples
### 1D 0th order ODE problem: Constant force
* [1D Dynamics with constant force](http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/Presentation/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/Presentation/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/Presentation/examples/Spreadsheets/1D_FreeFall_Basic/)
* [1D free fall example (version with named parameters)](http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/Presentation/examples/Spreadsheets/1D_FreeFall_NamedCells/)
* Processing ([see processing.org](https://processing.org/), and [try it online](https://editor.p5js.org/))
* [1D free fall](https://editor.p5js.org/vojtech.svob/sketches/p_VGqDX5)
* Python @ JupyterNotebook ([see jupyter.org](https://jupyter.org/) and [try it online](https://mybinder.org/v2/gh/jupyterlab/jupyterlab-demo/try.jupyter.org?urlpath=lab))
* [1D free fall](http://buon.fjfi.cvut.cz/raws/CTU4WP@ELAB/Presentation/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/Presentation/examples/Spreadsheets/1D_Pendulum_Basic/)
* [Pendulum with friction](http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/Presentation/examples/Spreadsheets/1D_Pendulum_Friction/)
* [Pendulum with friction - phase space](http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/Presentation/examples/Spreadsheets/1D_Pendulum_Friction_PhaseSpace/)
* [Pendulum - energy conservation analysis](http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/Presentation/examples/Spreadsheets/1D_Pendulum_EnergyConservation/)
* [Pendulum - small angle approximation analysis](http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/Presentation/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)
* Octave (see [Octave web](https://www.gnu.org/software/octave/))
* [Pendulum (basic version)](http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/Presentation/examples/octave/PendulumBasic/)
## 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)
### World pendulum
* [Processing](https://editor.p5js.org/vojtech.svob/sketches/ni4EgKh-)
## Final remarks
### 4th order Runge Kutta method (better alternative to Euler scheme)
* [VBA implementation](https://flylib.com/books/en/2.22.1/applying_the_runge_kutta_method_to_second_order_initial_value_problems.html)
### [Standard CAS functions to solve ODE problems ](Presentation/examples/PythonJupyterNotebook/Pendulum_odeint/)
* [Pendulum](http://buon.fjfi.cvut.cz/raws/CTU4WP@ELAB/Presentation/examples/PythonJupyterNotebook/Pendulum_odeint/model.html)
### 2D problem, a simple: Horizontal Launch
* [Spreadsheet approach](http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/Presentation/examples/Spreadsheets/2D_HorizontalLaunch_Basic/)
* [Processing approach](https://editor.p5js.org/vojtech.svob/sketches/3O2OUtpW)
### 2D problem, a bit complex: Foucault pendulum
* [Processing approach](https://editor.p5js.org/vojtech.svob/sketches/DMgIN9Cq)
### 2D problem, a bit complex: Satellite motion
* [Processing approach](https://editor.p5js.org/vojtech.svob/sketches/m57euT3SL)
## 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 9.80305
* Bogota 9.77347
* Lisbon 9.80088
* Marseille 9.80499
* Panama 9.78176
* Prague 9.81049
* Rio de Janeiro 9.78817
* Santiago de Chile (33°27' S) 9.79477 (FP@FCFM: 18.5 m, 100 kg)
* Punta Arenas (53°8'S) 9.81345
* Paris ( 48°52' N) 9.80961 (FP@Pantheon: 68 m, 28 kg)
* [wiki/Gravity_of_Earth](https://en.wikipedia.org/wiki/Gravity_of_Earth): Equator ( 0° ) 9.780
* [wiki/Gravity_of_Earth](https://en.wikipedia.org/wiki/Gravity_of_Earth): Poles ( +/- 90° ) 9.832
## 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)
* [Simulate the Motion of the Periodic Swing of a Pendulum @ MathWorks](https://www.mathworks.com/help/symbolic/examples/simulate-physics-pendulum-swing.html)
# Pendulum tracking
* Based on [openCV](https://opencv.org/) python library of programming functions mainly aimed at real-time computer vision.
* **[Link to Pendulum sandbox](http://buon.fjfi.cvut.cz/raws/WP@ELAB/Videonanalysis/Tracker.cv2/)**
* Based on the [openCV](https://opencv.org/) python library of programming functions mainly aimed at real-time computer vision.
* **[Link to the Pendulum sandbox](http://buon.fjfi.cvut.cz/raws/WP@ELAB/Videonanalysis/Tracker.cv2/)**
* An Alternative: Free video analysis and modeling tool [Tracker](https://physlets.org/tracker/)
## 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 )
