Deploying a Planar Elastic Rod System with Cable Elements Attached to a Spacecraft

A planar nonlinear problem of the dynamics of deployment of a rod system from one position to another is considered in this paper. The truss structure consists of elastic inextensible rods, connected at the ends by elastic nodal hinges that allow large angles of rotation. Between any two hinges, a tensile cable can be included as a link, the length of which can vary according to a given law in time. The rod system, whose motion is described in a moving coordinate system, is attached to a non-deformable spacecraft making movements and rotation relative to its center of gravity as a free solid body. The displacements of each rod are characterized by its finite rotation as a rigid body relative to a straight line passing through two adjacent hinge assemblies, and by a bend with a small transverse displacement. The equations of motion in velocities for the spacecraft and in the selected generalized coordinates for the rod system are obtained on the basis of the principle of possible displacements. The author examines the problems of unfolding the truss structure from one state to another, with tensile cables acting as position locking devices, due to elastic or inertial forces, as well as tension forces of the tensile cables of variable length.

References

[1] 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]. 1992, no. 1, pp. 177–180.

[2] 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]. 1992, no. 4, pp. 183–190.

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

[4] 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.

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

[6] Alpatov A.P., Beletskii V.V., Dranovskii V.I., Zakrzhevskii A.E., Pirozhenko A.V., Troger G., Khoroshilov V.S. Dinamika kosmicheskikh sistem s trosovymi i sharnirnymi soedineniiami [Dynamics of space systems with the cable and swivels]. Moscow-Izhevsk, Reguliarnaia i khaoticheskaia dinamika publ., 2007. 560 p.

[7] Ivanov V.A., Kupreev S.A., Ruchinskii V.S. Osobennosti dinamiki upravliaemogo funktsionirovaniia kosmicheskikh trosovykh sistem na krugovykh i ellipticheskikh orbitakh [Features of the dynamics of the controlled operation of space tethered systems in circular and elliptical orbits]. Moscow, MAI publ., 2016. 160 p.

[8] Ivanov V.A., Kupreev S.A., Ruchinskii V.S. Kosmicheskie trosovye sistemy [Space tether system]. Moscow, Al’fa-M publ., 2014. 208 p.

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

[10] Russkikh S.V. Ploskaia nelineinaia zadacha dinamiki transformiruemoi uprugoi sterzhnevoi sistemy, prisoedinennoi k kosmicheskomu apparatu [A Flat Nonlinear Problem of the Dynamics of a Transformable Elastic Rod System Attached to a Spacecraft]. Izvestiia vysshikh uchebnykh zavedenii. Mashinostroenie [Proceedings of Higher Educational Institutions. Маchine Building]. 2017, no. 11, pp. 89–100.

[11] Grishanina T.V., Shkliarchuk F.N. Dinamika ploskogo dvizheniia tela s sistemoi posledovatel’no soedinennykh uprugoviazkimi sharnirami gibkikh nerastiazhimykh sterzhnei pri bol’shikh uglakh povorota [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]. Izvestiia RAN. Mekhanika tverdogo tela [Mechanics of Solids]. 2011, no. 2(46), pp. 248–255.