One pendulum to run them all

@article{Barenboim2013OnePT,
  title={One pendulum to run them all},
  author={Gabriela Barenboim and Jos{\'e} Angel Oteo},
  journal={European Journal of Physics},
  year={2013},
  volume={34},
  pages={1049-1065}
}
The analytical solution for the three-dimensional linear pendulum in a rotating frame of reference is obtained, including Coriolis and centrifugal accelerations, and expressed in terms of initial conditions. This result offers the possibility of treating Foucault and Bravais pendula as trajectories of the same system of equations, each of them with particular initial conditions. We compare them with the common two-dimensional approximations in textbooks. A previously unnoticed pattern in the… Expand
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References

SHOWING 1-9 OF 9 REFERENCES
The Bravais pendulum: the distinct charm of an almost forgotten experiment
In the year 1851 in Paris, the apparent change of the plane of oscillation of a linear pendulum was observed by Leon Foucault. In the same year, at the same place, the unequal duration of theExpand
The Pendulum: A Case Study in Physics
The Life and Science of Léon Foucault: The Man who Proved the Earth Rotates
Foreword Preface Acknowledgements 1. Introduction 2. Early years 3. The metallic eye: photography 4. The 'delicious pastime' applied to science 5. The beautiful science of optics 6. Order, precisionExpand
Nineteen Dubious Ways to Compute the Exponential of a Matrix
In principle, the exponential of a matrix could be computed in many ways. Methods involving approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polyn...
The Theory of Matrices
Volume 2: XI. Complex symmetric, skew-symmetric, and orthogonal matrices: 1. Some formulas for complex orthogonal and unitary matrices 2. Polar decomposition of a complex matrix 3. The normal form ofExpand
Traité de méchanique rationelle , vol . 2 , p . 296 ( Gauthier – Villars . Paris )
  • 1953
Traité de méchanique rationelle, vol.2, p.296 (Gauthier–Villars
  • 1953
The Foucault Pendulum Star Path and the n-Leaved Rose
On Foucault's Pendulum