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A Brief Analysis of Artificial Satellites Solar Panels Deployment Considering a Nonlinear Dynamic Model

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Nonlinear Mechanics of Complex Structures

Abstract

The present analysis is focused on the nonlinear dynamics of a solar panel opening during the trajectory of a satellite around the Earth, analyzing the dynamics between energy sources and structural response that must not be ignored in real engineering problems. The governing equations were obtained with the Lagrangian function and the results were found using the Runge–Kutta method for integration. These results were found using two different models. One of them considers the panel directly connected to a DC motor and the other considers a torsion spring connected to the motor shaft and the solar panel. As a result, we obtained the time series of the mathematical model proposed.

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References

  • Avanço, R.H., Tusset, A.M., Balthazar, J.M., et al.: On nonlinear dynamics behavior of an electro-mechanical pendulum excited by a non-ideal motor and a chaos control taking into account parametric errors. J Braz. Soc. Mech. Sci. Eng. 40, 23 (2018). https://doi.org/10.1007/s40430-017-0955-x

    Article  Google Scholar 

  • Balthazar, J.M., Brasil, R.M.I.R.F., Weber, H.I., Fenili, A., Belato, D., Felix, J.L.P.: An overview on non-ideal vibrations. Meccanica 38, 613–621 (2003)

    Article  Google Scholar 

  • Balthazar, J.M., Tusset, A.M., Brasil, R.M.L.R.F., et al.: An overview on the appearance of the Sommerfeld effect and saturation phenomenon in non-ideal vibrating systems (NIS) in macro and MEMS scales. Nonlinear Dyn. 93, 19–40 (2018)

    Article  Google Scholar 

  • Budynas, R.G., Nisbett, K.: Shigley’s Mechanical Engineering Design. McGraw-Hill (2014). ISBN-10:9780073398204

    Google Scholar 

  • Crawford Jr., F.S.: Waves (Berkeley Physics Course, vol. 3) McGraw-Hill (1968). ISBN 10:0070048606

    Google Scholar 

  • Cveticanin, L., Zukovic, M., Balthazar, J.M.: Dynamics of Mechanical Systems with Non-Ideal Excitation. Springer International Publishing (2018). ISBN: 978-3-319-54168-6

    Google Scholar 

  • Dormand, J., Prince, P.: A family of embedded Runge-Kutta formulae. J. Comput. Appl. Math. 6, 19–26 (1980)

    Article  MathSciNet  Google Scholar 

  • Fenili, A.: Modelagem Matemática e Análise dos Comportamentos Ideal e Não Ideal de Estruturas Flexíveis de Rastreamento. Phd Thesis, UNICAMP, Campinas, SP (2000)

    Google Scholar 

  • Kononenko, V.O.: Vibrating system with a limited power-supply. Iliffe, London (1969)

    Google Scholar 

  • Krasnopol’skaya, T.S., Shvets, A.Y.: Chaotic interactions in a pendulum-energy-source system. Prikl. Mekh. 26(5), 90–96 (1990)

    MATH  Google Scholar 

  • Krasnopol’skaya, T.S., Shvets, A.Y.: Chaotic oscillations of a spherical pendulum as an example of interaction with energy source. Int. Appl. Mech. 28, 669–674 (1992)

    Article  Google Scholar 

  • Maxongroup Ec 90 flat (2020). https://www.maxongroup.com/medias/sys_master/root/8841186181150/EN-302.pdf

  • Omidi, E., Mahmoodi, S.N.: Nonlinear vibration suppression of flexible structures using nonlinear modified positive position feedback approach. Nonlinear Dyn. 79, 835–849 (2015). https://doi.org/10.1007/s11071-014-1706-5

    Article  MATH  Google Scholar 

  • Porro, J.R.S.; Fenili A.; Balthazar, J.M.: Modelagem Matemática de um Satélite Considerando a Abertura de um Painel Solar: Abordagem Ideal e Não-Ideal. In: CONEM 2004—III Congresso Nacional de Engenharia Mecânica, Belém, PA, Brazil. In: Proceedings of the CONEM 2004—III Congresso Nacional de Engenharia Mecânica (in portuguese) (2004)

    Google Scholar 

  • Soler, T., Eisemann, D.W.: Determination of look angles to geostationary communication satellites. J. Surveying Eng. 120(3), 123 (1994). https://doi.org/10.1061/(ASCE)0733-9453(1994)120:3(115).ISSN0733-9453

    Article  Google Scholar 

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Acknowledgements

The third and fourth authors are grateful for the financial support by the Brazilian Council for Scientific and Technological Development, CNPq, grants 306525/2015-1 and 307371/2017-4, respectively.

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Correspondence to José Manoel Balthazar .

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Avanço, R. et al. (2021). A Brief Analysis of Artificial Satellites Solar Panels Deployment Considering a Nonlinear Dynamic Model. In: Altenbach, H., Amabili, M., Mikhlin, Y.V. (eds) Nonlinear Mechanics of Complex Structures. Advanced Structured Materials, vol 157. Springer, Cham. https://doi.org/10.1007/978-3-030-75890-5_21

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