A Flat Nonlinear Problem of the Dynamics of a Transformable Elastic Rod System Attached to a Spacecraft

The nonlinear dynamics of a flat transformable rod system consisting of elastic inextensible rods, connected to each other at the ends by elastic-viscous nodal hinges allowing for large angles of rotation, is considered in this article. The rod system is attached to a nondeformable spacecraft that undergoes displacements and turns relative to its center of gravity as a free solid body. The motion of the considered system is described in a moving coordinate system. The displacements of each rod are characterized by the rod’s final turning as a solid body relative to a straight line passing through two neighbouring hinge nodes, and by a bend with a small transverse displacement. Equations of motion in velocities for a space vehicle and in selected generalized coordinates for a rod system are obtained. The equations are derived based on the principle of possible displacements. The equations are used to solve the problems of deployment of the rod system from one position to another by engaging elastic-viscous clamps integrated into the hinges, due to elastic, centrifugal and inertial forces.

References

[1] Svetlitskii V.A. Mekhanika sterzhne. Chast’ 2. Dinamika [Mechanics of rods. Pt. 2. Dynamics]. Moscow, Vysshaia shkola publ., 1987. 304 p.

[2] Svetlitskii V.A. Mekhanika absoliutno gibkikh sterzhnei [Mechanics of absolutely flexible rods]. Moscow, MAI publ., 2001. 432 p.

[3] Dokuchaev L.V. Nelineinaia dinamika letatel’nykh apparatov s deformiruemymi elementami [Nonlinear dynamics of aircraft with deformable elements]. Moscow, Mashinostroenie publ., 1987. 232 p.

[4] Shkliarchuk F.N. Nelineinye i linearizovannye uravneniia dvizheniia uprugikh kosmicheskikh konstruktsii [Nonlinear and linearized equations of motion of a flexible space structures]. Izvestiia RAN. Mekhanika tverdogo tela [Mechanics of Solids a Journal of Russian Academy of Sciences]. 1996, no. 1, pp. 161–175.

[5] Grishanina T.V., Shkliarchuk F.N. Dinamika uprugikh upravliaemykh konstruktsii [Driven dynamics of elastic structures]. Moscow, MAI publ., 2007. 328 p.

[6] Grishanina T.V., Shklyarchuk F.N. Dynamics of plane motion of a body with a system of flexible inextensible rods connected in series by elastoviscous joints at large angles of rotation. Mechanics of Solids, 2011, vol. 46, no. 2, pp. 248–255.

[7] Ibrahim A.M., Modi V.J. A formulation for studying dynamics of N connected flexible deployable members. Acta Astronautica, 1987, vol. 16, pp. 151–164.

[8] Wie B., Furumoto N., Banerjee A.K., Barba P.M. Modeling and simulation of spacecraft solar array deployment. AIAA Journal of Guidance, Control and Dynamics, 1986, vol. 9, no. 5, pp. 593–598.

[9] Panichkin V.I. Matematicheskoe modelirovanie dinamiki raskrytiia mnogostvorchatoi solnechnoi batarei [Mathematical modelling of the deployment dynamics of multi-leaf solar panels]. Izvestiia RAN. Mekhanika tverdogo tela [Mechanics of Solids a Journal of Russian Academy of Sciences]. 1992, no. 1, pp. 177–180.

[10] Panichkin V.I. Matematicheskoe modelirovanie dinamiki deformirovaniia mnogostvorchatoi solnechnoi batarei v protsesse raskrytiia [Mathematical modeling of dynamics of deformation of the multi-leaf solar panels in the erection process]. Izvestiia RAN. Mekhanika tverdogo tela [Mechanics of Solids a Journal of Russian Academy of Sciences]. 1992, no. 4, pp. 183–190.

[11] Borzykh S.V., Shchiblev Iu.N., Ososov N.S. Dinamika raskrytiia krupnogabaritnykh solnechnykh batarei [The dynamics of the disclosure of large solar panels]. Raketno-kosmicheskaia tekhnika [Aerospace technology]. 2008, ser. 12, is. 1, pp. 144–158.

[12] Krylov A.V., Churilin S.A. Modelirovanie raskrytiia solnechnykh batarei razlichnykh konfiguratsii [Simulation of Deployment of Solar Batteries with Various Configurations]. Vestnik MGTU. Seriia Mashinostroenie [Herald of the Bauman Moscow State Technical University. Ser. Mechanical Engineering]. 2011, no. 1, pp. 106–112.

[13] Iudintsev V.V. Modelirovanie protsessov raskrytiia mnogoelementnykh konstruktsii kosmicheskikh apparatov [Modelling of the Spacecraft’s Multibody Construction Deployment Process]. Polet [Flight]. 2012, no. 5, pp. 28–33.

[14] Bakulin V.N., Borzykh S.V., Il’iasova I.R. Matematicheskoe modelirovanie protsessa raskrytiia mnogozvennykh solnechnykh batarei [Mathematical simulation of opening process of multy-element solar battery]. Vestnik MAI [Vestnik Moskovskogo aviatsionnogo instituta]. 2011, vol. 18, no. 3, pp. 295–302.

[15] Russkikh S.V. Nelineinaia dinamika kosmicheskogo apparata s prisoedinennoi uprugoi sterzhnevoi sistemoi [Nonlinear Dynamics of a Space Vehicle with an Attached Elastic Rod System]. Izvestiia vysshikh uchebnykh zavedenii. Mashinostroenie [Proceedings of Higher Educational Institutions. Маchine Building]. 2017, no. 7, pp. 81–89.