# Research of the solar sail surface cloth form during it’s spatial spread

### Аuthors

Makarenkova N. A.

e-mail: hope150392@mail.ru

### Abstract

The spatial spread of the solar sail, in which the shape of the surface of the membrane is maintained by centrifugal forces, is considered. A mathematical model of the solar sail is represented as a set of approximating circles connected by a thin stretched weightless membrane [3]. The surface shape of the rotating membrane in the case effect of the sunlight pressure on the membrane is investigated. Since the membrane deviation is a minor value compared with its radius, the pressure effect of the sunlight on the surface shape of the solar sail cloth in the further investigation was not considered. Also, the surface shape of the solar sail in the case of a uniform rotary motion in the time of its reorientation was simulated. Dependences of deviation of the outer edge of the membrane from the plane, in which the rigid insert lies, at different radiuses of the rigid insert and at different angular velocities were constructed. The problem of the active damping of the membrane fluctuations was considered. A finite-dimensional system obtained as a result of the approximation of the membrane by several circles, was investigated. The roots of its characteristic polynomial, which determine the natural frequencies of the membrane fluctuations, turned out to be greatly separated from each other. In this regard, only the first non-zero frequency was solved to damp. Control law, which transfers the roots of the characteristic polynomial in the left half-plane and provides damping, was suggested. Transients by the angels, that define the spatial position of the solar sail, were obtained in the case the shift of the roots to the left half-plane.

### Keywords:

solar sail, elastic mode control, the surface shape of the rotating membrane

### References

1. Komkov V.A. Mel’nikov V.M. Tsentrobezhnye beskarkasnye krupnogabaritnye kosmicheskie konstruktsii (Centrifugal frameless large-size space designs), Moscow, FIZMATLIT, 2009, 447 p.

2. Stepaniants G.A. Modeling, measurement & control, AM SE Press, 1993, vol. 51, no. 3, pp. 1-12.

3. Polyakhova E. N. Kosmicheskii polet solnechnym parusom: problemy i perspektivy (Space flight with the solar sail: problems and perspectives), Moscow, Nauka, 1986, 303 p.

4. Stepan’yants G.A. Aviakosmicheskoe priborostroenie, 2002, no. 3, pp. 10-15.

5. Anisimov V.M., Tret’yakova O.N. Prakticheskii kurs fiziki. Osnovy kvantovoi fiziki (Practical course of physics. Fundamentals of quantum physics), Moscow, MAI, 2005, 161 p.

6. Legostaev V.P., Subbotin A.V., Timakov S.N., Zykov A.V. Trudy MFTI, 2011,vol. 3, no.3. pp. 73-78.

7. Timoshenko S.P. Teoriya uprugosti (The theory of elasticity), Moscow, Nauka, 1937, 451 p.

8. Grishanin Yu.S., Lebedev G.N., Lipatov A.V., Stepan’yants G.A. Teoriya optimal’nykh system (The theory of optimal systems), Moscow, MAI, 1999, 317 p.