Calculus for the WP@ELAB training

mail to main author Vojtech Svoboda

• The presentation
• NEW:: The November 2021 overview
• Directory of all the relevant stuff (latex source, figs, simulations, etc.)
• Resources
• Examples
• all in zip

Examples

1D 0th order ODE problem: Constant force

• 1D Dynamics with constant force

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

• 1D Dynamics with friction force

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

• Spreadsheets
  • 1D free fall example (basic version)
  • 1D free fall example (version with named parameters)
• Processing (see processing.org, and try it online)
  • 1D free fall
• Python @ JupyterNotebook (see jupyter.org and try it online)
  • 1D free fall

1D 2nd order ODE problem: Pendulum (full dynamics)

• Spreadsheets
  • Pendulum (basic version)
  • Pendulum with friction
  • Pendulum with friction - phase space
  • Pendulum - energy conservation analysis
  • Pendulum - small angle approximation analysis
• Processing (see processing.org, try it)
  • pendulum (basic version)
  • pendulum (“advanced” version)
  • pendulum with friction
  • two pendulums (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)
  • Pendulum (basic version)

Simulation and experiment

Prague

• Pendulum in Prague (Charles university)
• Processing

World pendulum

• Processing

Final remarks

4th order Runge Kutta method (better alternative to Euler scheme)

• VBA implementation

Standard CAS functions to solve ODE problems

• Pendulum

2D problem, a simple: Horizontal Launch

• Spreadsheet approach
• Processing approach

2D problem, a bit complex: Foucault pendulum

• Processing approach

2D problem, a bit complex: Satellite motion

• Processing approach

Relevant info

• Gravitational constants at important places from Local Acceleration of Gravity@Wolfram [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: Equator ( 0° ) 9.780
  • wiki/Gravity_of_Earth: Poles ( +/- 90° ) 9.832

References

• Daniel A. Russell: Oscillation of a Simple Pendulum (accessed March 2, 2020).
• Wikipedia contributors, “Pendulum (mathematics),” Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/w/index.php?title=Pendulum_(mathematics)&oldid=942104313 (accessed March 2, 2020).
• Local Acceleration of Gravity@Wolfram (accessed March 2, 2020).
• Simulate the Motion of the Periodic Swing of a Pendulum @ MathWorks

NEW: Pendulum tracking

• Based on the openCV python library of programming functions mainly aimed at real-time computer vision.

• Link to the Pendulum sandbox

• An Alternative: Free video analysis and modeling tool Tracker

Authors

• Vojtech Svoboda (Czech Technical University in Prague)
• Pavel Kuriscak (Charles University in Prague)
• Frantisek Lustig (Charles University in Prague)

http://buon.fjfi.cvut.cz/wp

Any comments, suggestions, ideas highly appreciated. Thanks in advance. Authors.