Skip to main content
SpringerLink
Log in

A review of dynamic analysis on space solar power station

  • Review Article
  • Published:
Astrodynamics Aims and scope Submit manuscript

Abstract

The concept of a space solar power station (SSPS) was proposed in 1968 as a potential approach for solving the energy crisis. In the past 50 years, several structural concepts have been proposed, but none have been sent into orbit. One of the main challenges of the SSPS is dynamic behavior prediction, which can supply the necessary information for control strategy design. The ultra-large size of the SSPS causes difficulties in its dynamic analysis, such as the ultra-low vibration frequency and large flexibility. In this paper, four approaches for the numerical analysis of the dynamic problems associated with the SSPS are reviewed: the finite element, absolute nodal coordinate, floating frame formulation, and structure-preserving methods. Both the merits and shortcomings of the above four approaches are introduced when they are employed in dynamic problems associated with the SSPS. Synthesizing the merits of the aforementioned four approaches, we believe that embedding the structure-preserving method into finite element software may be an effective way to perform a numerical analysis of the dynamic problems associated with the SSPS.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Glaser, P. E. Power from the Sun: Its future. Science, 1968, 162(3856): 857–861.

    Google Scholar 

  2. Glaser, P. E. Solar power via satellite. Astronautics & Aeronautics, 1973, 11(8): 60–68.

    Google Scholar 

  3. Mankins, J. C. A fresh look at space solar power: New architectures, concepts and technologies. Acta Astronautica, 1997, 41(4–10): 347–359.

    Google Scholar 

  4. Schwenk, F. C. Summary assessment of the satellite power system. Journal of Energy, 1983, 7(3): 193–199.

    Google Scholar 

  5. Donovan, P., Woodward, W., Cherry, W. E., Morse, F., Herwig, L. An assessment of solar energy as a national energy resource. Technical Report. College Park, USA: Department of Mechanical Engineering, Maryland University, 1972.

    Google Scholar 

  6. Hoffert, M. I., Caldeira, K., Benford, G., Criswell, D. R., Green, C., Herzog, H., Jain, A. K., Kheshgi, H. S., Lackner, K. S., Lewis, J. S. et al. Advanced technology paths to global climate stability: Energy for a greenhouse planet. Science, 2002, 298(5595): 981–987.

    Google Scholar 

  7. Office AC., HQ N., Office ASA., LeRC N. Space solar power, an advanced concepts study project. 1995.

  8. Saito, Y., Fujita, T., Mori, M. Summary of studies on space solar power systems of Japan Aerospace Exploration Agency (JAXA). In: Proceedings of the 57th International Astronautical Congress, Valencia, Spain, 2006: IAC-06-C3.1.04.

  9. Sogawa, T., Yamagiwa, Y. SPS 2000 Project Concept. 1993.

  10. Sasaki, S., Tanaka, K., Higuchi, K., Okuizumi, N., Kawasaki, S., Shinohara, N., Senda, K., Ishimura, K. A new concept of solar power satellite: Tethered-SPS. Acta Astronautica, 2007, 60(3): 153–165.

    Google Scholar 

  11. Seboldt, W., Klimke, M., Leipold, M., Hanowski, N. European sail tower SPS concept. Acta Astronautica, 2001, 48(5–12): 785–792.

    Google Scholar 

  12. Yang, C., Hou, X. B., Wang, L. Thermal design, analysis and comparison on three concepts of space solar power satellite. Acta Astronautica, 2017, 137: 382–402.

    Google Scholar 

  13. Yang, Y., Zhang, Y. Q., Duan, B. Y., Wang, D. X., Li, X. A novel design project for space solar power station (SSPS-OMEGA). Acta Astronautica, 2016, 121: 51–58.

    Google Scholar 

  14. Mankins, J., Kaya, N., Vasile, M. SPS-ALPHA: The first practical solar power satellite via arbitrarily large phased array (A 2011–2012 NIAC project). In: Proceedings of the 10th International Energy Conversion Engineering Conference, Atlanta, Georgia, USA, 2012: AIAA2012–3978.

  15. Glaser, P. E. Solar power satellite developments. Journal of the Astronautical Sciences, 1978, 26(2): 101–127.

    Google Scholar 

  16. Glaser, P. E. The earth benefits of solar power satellites. Space Solar Power Review, 1980, 1(1–2): 9–38.

    Google Scholar 

  17. Glaser, P. E. The solar power satellite—Past, present, and future. Space Solar Power Review, 1981, 2(1–2): 13–28.

    Google Scholar 

  18. Glaser, P. E. The solar power satellite—Progress so far. Interdisciplinary Science Reviews, 1982, 7(1): 14–29.

    Google Scholar 

  19. Hu, W. P., Zhang, C. Z., Deng, Z. C. Vibration and elastic wave propagation in spatial flexible damping panel attached to four special springs. Communications in Nonlinear Science and Numerical Simulation, 2020, 84: 105199.

    MathSciNet  MATH  Google Scholar 

  20. Hu, W. P., Yu, L. J., Deng, Z. C. Minimum control energy of spatial beam with assumed attitude adjustment target. Acta Mechanica Solida Sinica, 2020, 33(1): 51–60.

    Google Scholar 

  21. Hu, W. P., Yin, T. T., Zheng, W., Deng, Z. C. Symplectic analysis on orbit-attitude coupling dynamic problem of spatial rigid rod. Journal of Vibration and Control, 2020, 26(17–18): 1614–1624.

    MathSciNet  Google Scholar 

  22. Hu, W. P., Ye, J., Deng, Z. C. Internal resonance of a flexible beam in a spatial tethered system. Journal of Sound and Vibration, 2020, 475: 115286.

    Google Scholar 

  23. Hu, W. P., Song, M. Z., Deng, Z. C. Energy dissipation/transfer and stable attitude of spatial on-orbit tethered system. Journal of Sound and Vibration, 2018, 412: 58–73.

    Google Scholar 

  24. Hu, W. P., Deng, Z. C. Non-sphere perturbation on dynamic behaviors of spatial flexible damping beam. Acta Astronautica, 2018, 152: 196–200.

    Google Scholar 

  25. Hu, W. P., Li, Q. J., Jiang, X. H., Deng, Z. C. Coupling dynamic behaviors of spatial flexible beam with weak damping. International Journal for Numerical Methods in Engineering, 2017, 111(7): 660–675.

    MathSciNet  Google Scholar 

  26. Hu, W. P., Xi, X. J., Zhai, Z., Cui, P. F., Zhang, F., Deng, Z. C. Symplectic analysis on coupling behaviors of spatial flexible damping beam. Acta Mechanica Solida Sinica, 2022, 35(4): 541–551.

    Google Scholar 

  27. Wie, B., Roithmayr, C. M. Attitude and orbit control of a very large geostationary solar power satellite. Journal of Guidance, Control, and Dynamics, 2005, 28(3): 439–451.

    Google Scholar 

  28. Liu, Y. L., Wu, S. N., Zhang, K. M., Wu, Z. G. Gravitational orbit—attitude coupling dynamics of a large solar power satellite. Aerospace Science and Technology, 2017, 62: 46–54.

    Google Scholar 

  29. Zhao, Y., Zhang, J. R., Zhang, Y., Zhang, J., Hu, Q. Gravitational force and torque on a solar power satellite considering the structural flexibility. Acta Astronautica, 2017, 140: 322–337.

    Google Scholar 

  30. Ishimura, K., Higuchi, K. Coupling between structural deformation and attitude motion of large planar space structures suspended by multi-tethers. Acta Astronautica, 2007, 60(8–9): 691–710.

    Google Scholar 

  31. Turner, M. J., Clough, R. W., Martin, H. C., Topp, L. J. Stiffness and deflection analysis of complex structures. Journal of the Aeronautical Sciences, 1956, 23(9): 805–823.

    MATH  Google Scholar 

  32. Clough, R. The finite element method in plane stress analysis. In: Proceedings of the 2nd ASCE Conference on Electronic Computation, 1960.

  33. Ren, Q. W., Dong, Y. W., Yu, T. T. Numerical modeling of concrete hydraulic fracturing with extended finite element method. Science in China Series E: Technological Sciences, 2009, 52(3): 559–565.

    MATH  Google Scholar 

  34. Cremonesi, M., Frangi, A., Perego, U. A Lagrangian finite element approach for the simulation of water-waves induced by landslides. Computers & Structures, 2011, 89(11–12): 1086–1093.

    Google Scholar 

  35. Kapidžić, Z., Nilsson, L., Ansell, H. Finite element modeling of mechanically fastened composite-aluminum joints in aircraft structures. Composite Structures, 2014, 109: 198–210.

    Google Scholar 

  36. Wang, J., Xu, Y. J., Zhang, W. H. Finite element simulation of PMMA aircraft windshield against bird strike by using a rate and temperature dependent nonlinear viscoelastic constitutive model. Composite Structures, 2014, 108: 21–30.

    Google Scholar 

  37. Taleghani, B., Sleight, D., Muheim, D., Belvin, K., Wang, J. Assessment of analysis approaches for solar sail structural response. In: Proceedings of the 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Huntsville, Alabama, USA, 2003: AIAA 2003–4796.

  38. Yang, C., Hou, X. B., Wang, L. Parametric finite element modeling and design platform for SPS. Chinese Space Science and Technology, 2018, 38(3): 15–23. (in Chinese)

    Google Scholar 

  39. Yang, C., Zhang, X. P., Huang, X. Q., Cheng, Z. G., Zhang, X. H., Hou, X. B. Optimal sensor placement for deployable antenna module health monitoring in SSPS using genetic algorithm. Acta Astronautica, 2017, 140: 213–224.

    Google Scholar 

  40. Yang, C., Ma, R. Z., Ma, R. Optimal sensor placement for modal identification in multirotary-joint solar power satellite. IEEE Sensors Journal, 2020, 20(13): 7337–7346.

    Google Scholar 

  41. Shabana, A. A. Dynamics of Multibody Systems. Cambridge: Cambridge University Press, 2005.

    MATH  Google Scholar 

  42. Shabana, A. A. Flexible multibody dynamics: Review of past and recent developments. Multibody System Dynamics, 1997, 1(2): 189–222.

    MathSciNet  MATH  Google Scholar 

  43. Shabana, A. A., Hussien, H. A., Escalona, J. L. Application of the absolute nodal coordinate formulation to large rotation and large deformation problems. Journal of Mechanical Design, 1998, 120(2): 188–195.

    Google Scholar 

  44. Shabana, A. A. Definition of the slopes and the finite element absolute nodal coordinate formulation. Multibody System Dynamics, 1997, 1(3): 339–348.

    MathSciNet  MATH  Google Scholar 

  45. Shabana, A. A. Computer implementation of the absolute nodal coordinate formulation for flexible multibody dynamics. Nonlinear Dynamics, 1998, 16: 293–306.

    MathSciNet  MATH  Google Scholar 

  46. Berzeri, M., Shabana, A. A. Development of simple models for the elastic forces in the absolute nodal co-ordinate formulation. Journal of Sound and Vibration, 2000, 235(4): 539–565.

    Google Scholar 

  47. Omar, M. A., Shabana, A. A. A two-dimensional shear deformable beam for large rotation and deformation problems. Journal of Sound and Vibration, 2001, 243(3): 565–576.

    Google Scholar 

  48. Gerstmayr, J., Matikainen, M. K., Mikkola, A. M. A geometrically exact beam element based on the absolute nodal coordinate formulation. Multibody System Dynamics, 2008, 20(4): 359–384.

    MathSciNet  MATH  Google Scholar 

  49. Romero, I. A comparison of finite elements for nonlinear beams: The absolute nodal coordinate and geometrically exact formulations. Multibody System Dynamics, 2008, 20(1): 51–68.

    MathSciNet  MATH  Google Scholar 

  50. Shabana, A. A., Maqueda, L. G. Slope discontinuities in the finite element absolute nodal coordinate formulation: Gradient deficient elements. Multibody System Dynamics, 2008, 20(3): 239–249.

    MathSciNet  MATH  Google Scholar 

  51. Hussein, B. A., Weed, D., Shabana, A. A. Clamped end conditions and cross section deformation in the finite element absolute nodal coordinate formulation. Multibody System Dynamics, 2009, 21(4): 375–393.

    MATH  Google Scholar 

  52. Sanborn, G. G., Shabana, A. A. On the integration of computer aided design and analysis using the finite element absolute nodal coordinate formulation. Multibody System Dynamics, 2009, 22(2): 181–197.

    MATH  Google Scholar 

  53. Sanborn, G. G., Shabana, A. A. A rational finite element method based on the absolute nodal coordinate formulation. Nonlinear Dynamics, 2009, 58(3): 565–572.

    MathSciNet  MATH  Google Scholar 

  54. Orzechowski, G., Shabana, A. A. Analysis of warping deformation modes using higher order ANCF beam element. Journal of Sound and Vibration, 2016, 363: 428–445.

    Google Scholar 

  55. He, G., Patel, M., Shabana, A. Integration of localized surface geometry in fully parameterized ANCF finite elements. Computer Methods in Applied Mechanics and Engineering, 2017, 313: 966–985.

    MathSciNet  MATH  Google Scholar 

  56. Pappalardo, C. M., Wallin, M., Shabana, A. A. A new ANCF/CRBF fully parameterized plate finite element. Journal of Computational and Nonlinear Dynamics, 2017, 12(3): 031008.

    Google Scholar 

  57. Pappalardo, C. M., Wang, T. F., Shabana, A. A. On the formulation of the planar ANCF triangular finite elements. Nonlinear Dynamics, 2017, 89(2): 1019–1045.

    MathSciNet  MATH  Google Scholar 

  58. Shen, Z. X., Li, P., Liu, C., Hu, G. K. A finite element beam model including cross-section distortion in the absolute nodal coordinate formulation. Nonlinear Dynamics, 2014, 77(3): 1019–1033.

    Google Scholar 

  59. Tian, Q., Zhang, Y. Q., Chen, L. P., Qin, G. Advances in the absolute nodal coordinate method for the flexible multibody dynamics. Advances in Mechanics, 2010, 40(2): 189–202. (in Chinese)

    Google Scholar 

  60. Tian, Q., Chen, L. P., Zhang, Y. Q., Yang, J. Z. An efficient hybrid method for multibody dynamics simulation based on absolute nodal coordinate formulation. Journal of Computational and Nonlinear Dynamics, 2009, 4(2): 021009.

    Google Scholar 

  61. Liu, C., Tian, Q., Hu, H. Y. Efficient computational method for dynamics of flexible multibody systems based on absolute nodal coordinate. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(6): 1197–1205. (in Chinese)

    Google Scholar 

  62. Liu, C., Tian, Q., Hu, H. Y. New spatial curved beam and cylindrical shell elements of gradient-deficient absolute nodal coordinate formulation. Nonlinear Dynamics, 2012, 70(3): 1903–1918.

    MathSciNet  Google Scholar 

  63. Liu, C., Tian, Q., Yan, D., Hu, H. Y. Dynamic analysis of membrane systems undergoing overall motions, large deformations and wrinkles via thin shell elements of ANCF. Computer Methods in Applied Mechanics and Engineering, 2013, 258: 81–95.

    MathSciNet  MATH  Google Scholar 

  64. Yan, D., Liu, C., Tian, Q., Zhang, K., Liu, X. N., Hu, G. K. A new curved gradient deficient shell element of absolute nodal coordinate formulation for modeling thin shell structures. Nonlinear Dynamics, 2013, 74(1–2): 153–164.

    MathSciNet  Google Scholar 

  65. Luo, K., Liu, C., Tian, Q., Hu, H. Y. Nonlinear static and dynamic analysis of hyper-elastic thin shells via the absolute nodal coordinate formulation. Nonlinear Dynamics, 2016, 85(2): 949–971.

    MathSciNet  MATH  Google Scholar 

  66. Shen, Z. X., Tian, Q., Liu, X. N., Hu, G. K. Thermally induced vibrations of flexible beams using absolute nodal coordinate formulation. Aerospace Science and Technology, 2013, 29(1): 386–393.

    Google Scholar 

  67. Hu, W., Tian, Q., Hu, H. Y. Dynamic simulation of liquid-filled flexible multibody systems via absolute nodal coordinate formulation and SPH method. Nonlinear Dynamics, 2014, 75(4): 653–671.

    MathSciNet  Google Scholar 

  68. Wang, Q. T., Tian, Q., Hu, H. Y. Dynamic simulation of frictional contacts of thin beams during large overall motions via absolute nodal coordinate formulation. Nonlinear Dynamics, 2014, 77(4): 1411–1425.

    MathSciNet  Google Scholar 

  69. Zhao, J., Tian, Q., Hu, H. Y. Deployment dynamics of a simplified spinning IKAROS solar sail via absolute coordinate based method. Acta Mechanica Sinica, 2013, 29(1): 132–142.

    Google Scholar 

  70. Zhao, J., Liu, C., Tian, Q., Hu, H. Y. Dynamic analysis of spinning deployment of a solar sail composed of viscoelastic membranes. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(5): 746–754. (in Chinese)

    Google Scholar 

  71. Zhang, X. S., Zhang, D. G., Chen, S. J., Hong, J. Z. Several dynamic models of a large deformation flexible beam based on the absolute nodal coordinate formulation. Acta Physica Sinica, 2016, 65(9): 094501.

    Google Scholar 

  72. Li, Q. J., Deng, Z. C., Zhang, K., Huang, H. Unified modeling method for large space structures using absolute nodal coordinate. AIAA Journal, 2018, 56(10): 4146–4157.

    Google Scholar 

  73. Li, Q. J., Sun, T. T., Li, J. H., Deng, Z. C. Gravity-gradient-induced transverse deformations and vibrations of a Sun-facing beam. AIAA Journal, 2019, 57(12): 5491–5502.

    Google Scholar 

  74. Li, Q. J., Wei, Y., Deng, Z. C., Wu, Z. G., Jiang, J. P. Switched iterative learning attitude and structural control for solar power satellites. Acta Astronautica, 2021, 182: 100–109.

    Google Scholar 

  75. Luo, C. Q., Sun, J. L., Wen, H., Jin, D. P. Dynamics of a tethered satellite formation for space exploration modeled via ANCF. Acta Astronautica, 2020, 177: 882–890.

    Google Scholar 

  76. Pappalardo, C. M. A natural absolute coordinate formulation for the kinematic and dynamic analysis of rigid multibody systems. Nonlinear Dynamics, 2015, 81(4): 1841–1869.

    MathSciNet  MATH  Google Scholar 

  77. Li, Q. J., Deng, Z. C., Zhang, K., Wang, B. Precise attitude control of multirotary-joint solar-power satellite. Journal of Guidance, Control, and Dynamics, 2018, 41(6): 1435–1442.

    Google Scholar 

  78. Li, Q. J., Wang, B., Deng, Z. C., Ouyang, H. J., Wei, Y. A simple orbit-attitude coupled modelling method for large solar power satellites. Acta Astronautica, 2018, 145: 83–92.

    Google Scholar 

  79. Xu, X. M., Luo, J. H., Feng, X. G., Peng, H. J., Wu, Z. G. A generalized inertia representation for rigid multibody systems in terms of natural coordinates. Mechanism and Machine Theory, 2021, 157: 104174.

    Google Scholar 

  80. Vermaut, M., Naets, F., Desmet, W. A flexible natural coordinates formulation (FNCF) for the efficient simulation of small-deformation multibody systems. International Journal for Numerical Methods in Engineering, 2018, 115(11): 1353–1370.

    MathSciNet  Google Scholar 

  81. De Veubeke, B. F. The dynamics of flexible bodies. International Journal of Engineering Science, 1976, 14(10): 895–913.

    MATH  Google Scholar 

  82. Cavin, R. K., Dusto, A. R. Hamilton’s principle—Finite-element methods and flexible body dynamics. AIAA Journal, 1977, 15(12): 1684–1690.

    MATH  Google Scholar 

  83. Shabana, A. A., Schwertassek, R. Equivalence of the floating frame of reference approach and finite element formulations. International Journal of Non-Linear Mechanics, 1998, 33(3): 417–432.

    MATH  Google Scholar 

  84. Nada, A. A., Hussein, B. A., Megahed, S. M., Shabana, A. A. Use of the floating frame of reference formulation in large deformation analysis: Experimental and numerical validation. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-Body Dynamics, 2010, 224(1): 45–58.

    Google Scholar 

  85. Berzeri, M., Campanelli, M., Shabana, A. Definition of the elastic forces in the finite-element absolute nodal coordinate formulation and the floating frame of reference formulation. Multibody System Dynamics, 2001, 5(1): 21–54.

    MATH  Google Scholar 

  86. Gerstmayr, J. Strain tensors in the absolute nodal coordinate and the floating frame of reference formulation. Nonlinear Dynamics, 2003, 34(1–2): 133–145.

    MathSciNet  MATH  Google Scholar 

  87. Dibold, M., Gerstmayr, J., Irschik, H. A detailed comparison of the absolute nodal coordinate and the floating frame of reference formulation in deformable multibody systems. Journal of Computational and Nonlinear Dynamics, 2009, 4(2): 021006.

    Google Scholar 

  88. Lugrís, U., Naya, M. A., Luaces, A., Cuadrado, J. Efficient calculation of the inertia terms in floating frame of reference formulations for flexible multibody dynamics. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-Body Dynamics, 2009, 223(2): 147–157.

    Google Scholar 

  89. Khan, I. M., Ahn, W., Anderson, K. S., De, S. A logarithmic complexity floating frame of reference formulation with interpolating splines for articulated multi-flexible-body dynamics. International Journal of Non-Linear Mechanics, 2013, 57: 146–153.

    Google Scholar 

  90. Sherif, K., Nachbagauer, K. A detailed derivation of the velocity-dependent inertia forces in the floating frame of reference formulation. Journal of Computational and Nonlinear Dynamics, 2014, 9(4): 044501.

    Google Scholar 

  91. Hartweg, S., Heckmann, A. Moving loads on flexible structures presented in the floating frame of reference formulation. Multibody System Dynamics, 2016, 37(2): 195–210.

    MathSciNet  MATH  Google Scholar 

  92. Lozovskiy, A., Dubois, F. The method of a floating frame of reference for non-smooth contact dynamics. European Journal of Mechanics — A/Solids, 2016, 58: 89–101.

    MathSciNet  MATH  Google Scholar 

  93. Held, A., Knüfer, S., Seifried, R. Structural sensitivity analysis of flexible multibody systems modeled with the floating frame of reference approach using the adjoint variable method. Multibody System Dynamics, 2017, 40(3): 287–302.

    MathSciNet  MATH  Google Scholar 

  94. Orzechowski, G., Matikainen, M. K., Mikkola, A. M. Inertia forces and shape integrals in the floating frame of reference formulation. Nonlinear Dynamics, 2017, 88(3): 1953–1968.

    Google Scholar 

  95. Ellenbroek, M., Schilder, J. On the use of absolute interface coordinates in the floating frame of reference formulation for flexible multibody dynamics. Multibody System Dynamics, 2018, 43(3): 193–208.

    MathSciNet  MATH  Google Scholar 

  96. Schilder, J., Dwarshuis, K., Ellenbroek, M., Boer, A. The tangent stiffness matrix for an absolute interface coordinates floating frame of reference formulation. Multibody System Dynamics, 2019, 47(3): 243–263.

    MathSciNet  MATH  Google Scholar 

  97. Winkler, R., Gerstmayr, J. A projection-based approach for the derivation of the floating frame of reference formulation for multibody systems. Acta Mechanica, 2019, 230(1): 1–29.

    MathSciNet  MATH  Google Scholar 

  98. Held, A., Nowakowski, C., Moghadasi, A., Seifried, R., Eberhard, P. On the influence of model reduction techniques in topology optimization of flexible multibody systems using the floating frame of reference approach. Structural and Multidisciplinary Optimization, 2016, 53(1): 67–80.

    MathSciNet  Google Scholar 

  99. Wang, G. X. Dynamics analysis of parallel mechanism with flexible moving platform based on floating frame of reference formulation. Journal of Mechanisms and Robotics, 2019, 11(4): 041002.

    Google Scholar 

  100. Yamashita, H., Arora, R., Kanazawa, H., Sugiyama, H. Reduced-order thermomechanical modeling of multibody systems using floating frame of reference formulation. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-Body Dynamics, 2019, 233(3): 617–630.

    Google Scholar 

  101. Cammarata, A. Global flexible modes for the model reduction of planar mechanisms using the finite-element floating frame of reference formulation. Journal of Sound and Vibration, 2020, 489: 115668.

    Google Scholar 

  102. Cammarata, A., Pappalardo, C. M. On the use of component mode synthesis methods for the model reduction of flexible multibody systems within the floating frame of reference formulation. Mechanical Systems and Signal Processing, 2020, 142: 106745.

    Google Scholar 

  103. Huang, G. X., Zhu, W. D., Yang, Z. J., Feng, C., Chen, X. Reanalysis-based fast solution algorithm for flexible multi-body system dynamic analysis with floating frame of reference formulation. Multibody System Dynamics, 2020, 49(3): 271–289.

    MathSciNet  MATH  Google Scholar 

  104. Zwölfer, A., Gerstmayr, J. A concise nodal-based derivation of the floating frame of reference formulation for displacement-based solid finite elements. Multibody System Dynamics, 2020, 49(3): 291–313.

    MathSciNet  MATH  Google Scholar 

  105. Zwölfer, A., Gerstmayr, J. The nodal-based floating frame of reference formulation with modal reduction. Acta Mechanica, 2021, 232(3): 835–851.

    MathSciNet  MATH  Google Scholar 

  106. Zhang, K. M., Wu, S. N., Wu, Z. G. Robust enhanced control strategy of a solar power satellite using multiple sensors. Journal of Guidance, Control, and Dynamics, 2019, 43(2): 338–346.

    Google Scholar 

  107. Zhang, K. M., Wu, S. N., Wu, Z. G. Multibody dynamics and robust attitude control of a MW-level solar power satellite. Aerospace Science and Technology, 2021, 111: 106575.

    Google Scholar 

  108. Hamilton, W. R. On a general method in dynamics. Philosophical Transactions of the Royal Society of London, 1834, 124: 247–308.

    Google Scholar 

  109. Hamilton, W. R. Second essay on a general method in dynamics. Philosophical Transactions of the Royal Society of London, 1835, 125: 95–144.

    Google Scholar 

  110. Feng, K. On Difference Schemes and Symplectic Geometry. In: Proceedings of the 1984 Beijing Symposium on Differential Geometry and Differential Equations, 1985: 42–58.

  111. Feng, K. Difference-schemes for Hamiltonian-formalism and symplectic-geometry. Journal of Computational Mathematics, 1986, 4(3): 279–289.

    MathSciNet  MATH  Google Scholar 

  112. Ruth, R. D. A canonical integration technique. IEEE Transactions on Nuclear Science, 1983, 30(4): 2669–2671.

    Google Scholar 

  113. Hu, W. P., Huai, Y. L., Xu, M. B., Cao, P. X., Jiang, R. S., Shi, J. P., Deng, Z. C. Effects of tow parameters on dynamic behaviors of beam-type orbital debris. The Journal of the Astronautical Sciences, 2022, 69(1): 80–94.

    Google Scholar 

  114. Hu, W. P., Du, F., Zhai, Z., Zhang, F., Deng, Z. C. Symplectic analysis on dynamic behaviors of tethered tug-debris system. Acta Astronautica, 2022, 192: 182–189.

    Google Scholar 

  115. Fu, F. F. Symplectic Euler method for nonlinear high order Schrödinger equation with a trapped term. Advances in Applied Mathematics and Mechanics, 2019, 1(5): 699–710.

    MATH  Google Scholar 

  116. Hu, W. P., Song, M. Z., Deng, Z. C. Structure-preserving properties of Störmer—Verlet scheme for mathematical pendulum. Applied Mathematics and Mechanics, 2017, 38(9): 1225–1232.

    MathSciNet  Google Scholar 

  117. Sofroniou, M., Oevel, W. Sympletic Runge—Kutta shemes I: Order conditions. SIAM Journal on Numerical Analysis, 1997, 34(5): 2063–2086.

    MathSciNet  MATH  Google Scholar 

  118. Sanz-Serna, J. M. Symplectic Runge—Kutta and related methods: Recent results. Physica D: Nonlinear Phenomena, 1992, 60(1–4): 293–302.

    MathSciNet  MATH  Google Scholar 

  119. Sanz-Serna, J. M. Symplectic Runge—Kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review, 2016, 58(1): 3–33.

    MathSciNet  MATH  Google Scholar 

  120. Bridges, T. J. Multi-symplectic structures and wave propagation. Mathematical Proceedings of the Cambridge Philosophical Society, 1997, 121(1): 147–190.

    MathSciNet  MATH  Google Scholar 

  121. Marsden, J. E., Ratiu, T. S. Introduction to Mechanics and Symmetry. New York: Springer New York, 1999.

    MATH  Google Scholar 

  122. Marsden, J. E., Shkoller S. Multisymplectic geometry, covariant Hamiltonians, and water waves. Mathematical Proceedings of the Cambridge Philosophical Society, 1999, 125(3): 553–575.

    MathSciNet  MATH  Google Scholar 

  123. Reich, S. Multi-symplectic Runge—Kutta collocation methods for Hamiltonian wave equations. Journal of Computational Physics, 2000, 157(2): 473–499.

    MathSciNet  MATH  Google Scholar 

  124. Bridges, T. J., Reich, S. Multi-symplectic integrators: Numerical schemes for Hamiltonian PDEs that conserve symplecticity. Physics Letters A, 2001, 284(4–5): 184193.

    MathSciNet  MATH  Google Scholar 

  125. Bridges, T. J., Derks, G., Gottwald, G. Stability and instability of solitary waves of the fifth-order KdV equation: A numerical framework. Physica D: Nonlinear Phenomena, 2002, 172(1–4): 190–216.

    MathSciNet  MATH  Google Scholar 

  126. Wang, Y. S., Qin, M. Z. Multisymplectic schemes for the nonlinear Klein—Gordon equation. Mathematical and Computer Modelling, 2002, 36(9–10): 963–977.

    MathSciNet  MATH  Google Scholar 

  127. Moore, B., Reich, S. Backward error analysis for multi-symplectic integration methods. Numerische Mathematik, 2003, 95(4): 625–652.

    MathSciNet  MATH  Google Scholar 

  128. Moore, B. E., Reich, S. Multi-symplectic integration methods for Hamiltonian PDEs. Future Generation Computer Systems, 2003, 19(3): 395–402.

    Google Scholar 

  129. Hu, W. P., Deng, Z. C., Li, W. C. Multi-symplectic methods for membrane free vibration equation. Applied Mathematics and Mechanics, 2007, 28(9): 1181–1189. [130]_Hu, W. P., Deng, Z. C. Multi-symplectic method for generalized Boussinesq equation. Applied Mathematics and Mechanics, 2008, 29(7): 927–932.

    MathSciNet  MATH  Google Scholar 

  130. Hu, W. P., Deng, Z. C. Multi-symplectic method for generalized fifth-order KdV equation. Chinese Physics B, 2008, 17(11): 3923–3929.

    Google Scholar 

  131. Hu, W. P., Deng, Z. C., Han, S. M., Zhang, W. R. Generalized multi-symplectic integrators for a class of Hamiltonian nonlinear wave PDEs. Journal of Computational Physics, 2013, 235: 394–406.

    MathSciNet  MATH  Google Scholar 

  132. Hu, W. P., Wang, Z., Zhao, Y. P., Deng, Z. C. Symmetry breaking of infinite-dimensional dynamic system. Applied Mathematics Letters, 2020, 103: 106207.

    MathSciNet  MATH  Google Scholar 

  133. Hu, W. P., Xu, M. B., Song, J. R., Gao, Q., Deng, Z. C. Coupling dynamic behaviors of flexible stretching hub-beam system. Mechanical Systems and Signal Processing, 2021, 151: 107389.

    Google Scholar 

  134. Hu, W. P., Huai, Y. L., Xu, M. B., Feng, X. Q., Jiang, R. S., Zheng, Y. P., Deng, Z. C. Mechanoelectrical flexible hub-beam model of ionic-type solvent-free nanofluids. Mechanical Systems and Signal Processing, 2021, 159: 107833.

    Google Scholar 

Download references

Acknowledgements

The authors wish to thank Professor Chuanzeng Zhang of the University of Siegen, Germany, Professor Zhigang Wu and Doctor Qingjun Li of Sun Yat-sen University, China, and Doctor Gengxiang Wang of Peking University, China for providing several good suggestions. This research was supported by the National Natural Science Foundation of China (12172281, 11972284, 11672241, 11432010, and 11872303), Fund for Distinguished Young Scholars of Shaanxi Province (2019JC-29), Foundation Strengthening Program Technical Area Fund (2021-JCJQ-JJ-0565), Fund of the Science and Technology Innovation Team of Shaanxi (2022TD-61), and Fund of the Youth Innovation Team of Shaanxi Universities.

Author information

Authors and Affiliations

  1. School of Civil Engineering and Architecture, Xi’an University of Technology, Xi’an, 710048, China

    Weipeng Hu

  2. State Key Laboratory of Eco-Hydraulics in Northwest Arid Region of China, Xi’an University of Technology, Xi’an, 710048, China

    Weipeng Hu

  3. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an, 710072, China

    Zichen Deng

Authors
  1. Weipeng Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zichen Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Weipeng Hu.

Additional information

Declaration of competing interest

The authors have no competing interests to declare that are relevant to the content of this article.

Weipeng Hu is a distinguished professor at Xi’an University of Technology, China He is the leader of the “Key Dynamics and Control of the Advanced Equipment” Innovation Team of Shaanxi and leader of the “Dynamics and Control of the Solar Power Satellite System” Youth Innovation Team of Shaanxi Universities. His jobs were funded by the National Natural Science Foundation of China and the Shaanxi Outstanding Young Scientists Fund. He has received the first prize of 2017 Science and Technology Award of Shaanxi Universities and the first prize of 2018 Science and Technology Award of Shaanxi. E-mail: wphu@nwpu.edu.cn.

Zichen Deng is a distinguished professor of the Chang Jiang Scholars Program, a member of the Mechanics Discipline Review Group of the Academic Degree Commission of the State Council, China, and a member of the Advisory Committee for Mechanics Speciality, Ministry of Education, China. He is the dean of the School of Aeronautics and Director of Key Laboratory for Dynamics and Control of Complex Systems, Ministry of Industry and Information Technology, China. E-mail: dweifan@nwpu.edu.cn.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, W., Deng, Z. A review of dynamic analysis on space solar power station. Astrodyn 7, 115–130 (2023). https://doi.org/10.1007/s42064-022-0144-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42064-022-0144-2

Keywords

Search

Navigation