Planar heliocentric roto-translatory motion of a spacecraft with a solar sail of complex shape

A complete treatment of the general motion of rotation and translation of a solar-sail spacecraft is proposed for the non-flat sail of complex shape. The planar heliocentric roto-translatory motion is considered, orbit-rotational coupling in the problem of altitude and orbital sail motion is investigated for the two-folding sail formed by two unequal reflective rectangular plates oriented at a right angle. The problem of orbit-rotational coupling is essentially a planar one: both sail plates are orthogonal to the orbital plane. The possibility of the non-controlled interplanetary transfer with such two-folding sail at its passive radiational orientation is established analytically from point of view of orbit-rotational coupling. Optimal geometric proportions of this sail are found at minimum-time interplanetary transfers.