Abstract
In this paper, the attitude evolution of a dual-liquid-filled spacecraft with internal energy dissipation is investigated. The dynamic equations of the spacecraft system are established to study various trajectories including major axis spin, period-n limit cycle, and chaotic motion. A criterion is obtained by Melnikov’s method to predict the occurrence of chaotic motion of the system. The effects of system parameters, especially liquid parameters, on the chaotic region, are discussed in detail. The comparison of analytical and numerical results shows that our criterion can accurately separate the chaotic from nonchaotic region of the system in parameter space. Therefore, this paper contributes to avoid the potentially periodic and chaotic motions of spacecraft.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Hughes, P.C.: Spacecraft Attitude Dynamics. Wiley, New York (1986)
Liu, Y.Z., Chen, L.Q.: Chaos in Attitude Dynamics of Spacecraft. Springer, Berlin (2013)
Bracewell, R.N., Garriott, O.K.: Rotation of artificial earth satellites. Nature 182(4638), 760–762 (1958)
Melnikov, V.K.: On the stability of a center for time periodic perturbations. Trans. Mosc. Math. Soc. 12, 3–52 (1963)
Yam, Y., Mingori, D.L., Halsmer, D.M.: Stability of a spinning axisymmetric rocket with dissipative internal mass motion. J. Guidance Control Dyn. 20(2), 306–312 (1997)
Tong, X., Tabarrok, B.: Bifurcation of self-excited rigid bodies subjected to small perturbation torques. J. Guidance Control Dyn. 20(1), 605–615 (1997)
Or, A.C.: Chaotic motions of a dual-spin body. J. Appl. Mech. 65(1), 150–156 (1998)
Chen, L.Q., Liu, Y.Z.: Chaotic attitude motion of a magnetic rigid spacecraft and its control. Int. J. Non-Linear Mech. 37(3), 493–504 (2002)
Meehan, P.A., Asokanthan, S.F.: Control of chaotic instability in a dual-spin spacecraft with dissipation using energy methods. Multibody Syst. Dyn. 7(2), 171–188 (2002)
Meehan, P.A., Asokanthan, S.F.: Analysis of chaotic instabilities in a rotating body with internal energy dissipation. Int. J. Bifurc. Chaos 16(1), 1–19 (2006)
Kuang, J., Leung, A.Y.T., Tan, S.: Hamiltonian and chaotic attitude dynamics of an orbiting gyrostat satellite under gravity-gradient torques. Physica D 186(1–2), 1–19 (2003)
Shirazi, K.H., Ghaffari-Saadat, M.H.: Bifurcation and chaos in an apparent-type gyrostat satellite. Nonlinear Dyn. 39, 259–274 (2005)
Iñarrea, M.: Chaotic pitch motion of a magnetic spacecraft with viscous drag in an elliptical polar orbit. Int. J. Bifurc. Chaos 21(7), 1959–1975 (2011)
Aslanov, V.S., Ledkov, A.S.: Chaotic motion of a reentry capsule during descent into the atmosphere. J. Guidance Control Dyn. 39(8), 1834–1843 (2016)
Liu, J., Chen, L., Cui, N.: Solar sail chaotic pitch dynamics and its control in earth orbits. Nonlinear Dyn. 90(3), 1755–1770 (2017)
Gray, G.L., Kammer, D.C., Dobson, I.: Heteroclinic bifurcations in rigid bodies containing internally moving parts and a viscous damper. J. Appl. Mech. 66(3), 720–728 (1999)
Miller, A.J., Gray, G.L.: Nonlinear spacecraft dynamics with a flexible appendage, damping, and moving internal submasses. J. Guidance Control Dyn. 24(3), 605–615 (2001)
Yue, B.: Study on the chaotic dynamics in attitude maneuver of liquid-filled flexible spacecraft. AIAA J. 49(10), 2090–2099 (2011)
Nichkawde, C., Harish, P.M., Ananthkrishnan, N.: Stability analysis of a multibody system model for coupled slosh-vehicle dynamics. J. Sound Vib. 275(3–5), 1069–1083 (2004)
Kuang, L.K., Meehan, P.A., Leung, A.Y.T.: On the chaotic rotation of a liquid-filled gyrostat via the Melnikov-Holmes-Marsden integral. Int. J. Non-Linear Mech. 41, 475–490 (2006)
Zhou, L., Chen, Y., Chen, F.: Stability and chaos of a damped satellite partially filled with liquid. Acta Astronaut. 65(11–12), 1628–1638 (2009)
Chegini, M., Sadati, H., Salarieh, H.: Chaos analysis in attitude dynamics of a flexible satellite. Nonlinear Dyn. 93(3), 1421–1438 (2018)
Chegini, M., Sadati, H.: Chaos analysis in attitude dynamics of a satellite with two flexible panels. Int. J. Non-Linear Mech. 103, 55–67 (2018)
Chegini, M., Sadati, H., Salarieh, H.: Analytical and numerical study of chaos in spatial attitude dynamics of a satellite in an elliptic orbit. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 233(2), 561–577 (2019)
Doroshin, A.V.: Heteroclinic dynamics and attitude motion chaotization of coaxial bodies and dual-spin spacecraft. Commun. Nonlinear Sci. Numer. Simul. 17(3), 1460–1474 (2012)
Doroshin, A.V.: Chaos as the hub of systems dynamics. the part I–the attitude control of spacecraft by involving in the heteroclinic chaos. Commun. Nonlinear Sci. Numer. Simul. 59, 47–66 (2018)
Holmes, P.J., Marsden, J.E.: Horseshoes and Arnold diffusion for Hamiltonian systems on Lie groups. Indiana Univ. Math. J. 32(2), 273–309 (1983)
Rosenstein, M.T., Collins, J.J., De Luca, C.J.: A practical method for calculating largest Lyapunov exponents from small data sets. Physica D 65(1–2), 117–134 (1993)
Acknowledgements
This work was supported by the Natural Science Foundation of China (Grant Nos. 11772187 and 11802174) and the China Postdoctoral Science Foundation (Grant No. 2018M632104).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Liu, Y., Liu, X., Cai, G. et al. Attitude evolution of a dual-liquid-filled spacecraft with internal energy dissipation. Nonlinear Dyn 99, 2251–2263 (2020). https://doi.org/10.1007/s11071-019-05440-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-019-05440-5