A Short Vector Solution of the Foucault Pendulum Problem

Affiliation(s)

^{1}
Department of Medical Informatics and Biostatistics, University of Medicine and Pharmacy “Gr. T. Popa”,
Iasi, Romania.

^{2}
Department of Theoretical Mechanics, Technical University of Iasi, Iasi, Romania.

ABSTRACT

The paper studies the motion of the Foucault Pendulum in a rotating non-inertial reference frame and provides a closed form vector solution determined by vector and matrix calculus. The solution is determined through vector and matrix calculus in both cases, for both forms of the law of motion (for the Foucault Pendulum Problem and its “Reduced Form”). A complex vector which transforms the motion equation in a first order differential equation with constant coefficients is used. Also, a novel kinematic interpretation of the Foucault Pendulum motion is given.

The paper studies the motion of the Foucault Pendulum in a rotating non-inertial reference frame and provides a closed form vector solution determined by vector and matrix calculus. The solution is determined through vector and matrix calculus in both cases, for both forms of the law of motion (for the Foucault Pendulum Problem and its “Reduced Form”). A complex vector which transforms the motion equation in a first order differential equation with constant coefficients is used. Also, a novel kinematic interpretation of the Foucault Pendulum motion is given.

KEYWORDS

Foucault Pendulum, Non-Inertial Reference Frame, Closed Form Vector Solution, Complex Vector

Foucault Pendulum, Non-Inertial Reference Frame, Closed Form Vector Solution, Complex Vector

Cite this paper

Ciureanu, I. and Condurache, D. (2015) A Short Vector Solution of the Foucault Pendulum Problem.*World Journal of Mechanics*, **5**, 7-19. doi: 10.4236/wjm.2015.52002.

Ciureanu, I. and Condurache, D. (2015) A Short Vector Solution of the Foucault Pendulum Problem.

References

[1] Foucault, J.B.L. (1851) Physical Demonstration of the Rotation of the Earth by Means of the Pendulum. Comptes Rendus de l’Académie des Sciences de Paris, 51, 350-353.

[2] Anonymous (1851) On Foucault’s Pendulum Experiments. Journal of the Franklin Institute, 52, 419-421.

[3] Condurache, D. and Martinusi, V. (2007) Relative Spacecraft Motion in a Central Force Field. AIAA Journal of Guidance, Control and Dynamics, 30, 873-876.

http://dx.doi.org/10.2514/1.26361

[4] Condurache, D. and Martinusi, V. (2008) Exact Solution to the Relative Orbital Motion in a Central Force Field. The 2nd International Symposium on Systems and Control in Aeronautics and Astronautics, Shenzhen.

[5] Arnold, V. (1989) Mathematical Methods of Classical Mechanics. New York. (Translated from the 1974 Russian Original by K. Vogtmann and A. Weinstein, Springer, Berlin.)

[6] Appell, P. (1926) Traité de Mécanique Rationelle. 5 Volumes, Gauthier-Villars, Paris.

[7] Levi-Civita, T. and Amaldi, U. (1922-1926) Lezioni di mecanica razionale. N. Zanichelli (Ed.).

[8] Lurie, A.I. (2002) Analytical Mechanics. Springer, Berlin, 864.

http://dx.doi.org/10.1007/978-3-540-45677-3

[9] Condurache, D. and Matcovschi, M.-H. (1997) An Exact Solution to Foucault’s Pendulum Problem. Buletinul Institutului Politehnic Din Iasi, XLI (XLVII), 83-92.

[10] Goldstein, H., Poole, C.P. and Safko, J.L. (2002) Classical Mechanics. 3rd Edition, Addison-Wesley, Reading.

[11] Landau, L. and Lifschitz, E. (1981) Mécanique. Mir, Moscou.

[1] Foucault, J.B.L. (1851) Physical Demonstration of the Rotation of the Earth by Means of the Pendulum. Comptes Rendus de l’Académie des Sciences de Paris, 51, 350-353.

[2] Anonymous (1851) On Foucault’s Pendulum Experiments. Journal of the Franklin Institute, 52, 419-421.

[3] Condurache, D. and Martinusi, V. (2007) Relative Spacecraft Motion in a Central Force Field. AIAA Journal of Guidance, Control and Dynamics, 30, 873-876.

http://dx.doi.org/10.2514/1.26361

[4] Condurache, D. and Martinusi, V. (2008) Exact Solution to the Relative Orbital Motion in a Central Force Field. The 2nd International Symposium on Systems and Control in Aeronautics and Astronautics, Shenzhen.

[5] Arnold, V. (1989) Mathematical Methods of Classical Mechanics. New York. (Translated from the 1974 Russian Original by K. Vogtmann and A. Weinstein, Springer, Berlin.)

[6] Appell, P. (1926) Traité de Mécanique Rationelle. 5 Volumes, Gauthier-Villars, Paris.

[7] Levi-Civita, T. and Amaldi, U. (1922-1926) Lezioni di mecanica razionale. N. Zanichelli (Ed.).

[8] Lurie, A.I. (2002) Analytical Mechanics. Springer, Berlin, 864.

http://dx.doi.org/10.1007/978-3-540-45677-3

[9] Condurache, D. and Matcovschi, M.-H. (1997) An Exact Solution to Foucault’s Pendulum Problem. Buletinul Institutului Politehnic Din Iasi, XLI (XLVII), 83-92.

[10] Goldstein, H., Poole, C.P. and Safko, J.L. (2002) Classical Mechanics. 3rd Edition, Addison-Wesley, Reading.

[11] Landau, L. and Lifschitz, E. (1981) Mécanique. Mir, Moscou.