CTU4WP@ELAB/index

Calculus for the WP@ELAB training

Examples

1D 0th order ODE problem: Constant force

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

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

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

Simulation and experiment

Prague

World pendulum

Final remarks

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

Standard CAS functions to solve ODE problems

2D problem, a simple: Horizontal Launch

2D problem, a bit complex: Foucault pendulum

2D problem, a bit complex: Satellite motion

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

NEW: Pendulum tracking

Authors

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