On changing the independent variable from t to 0, the subsequent non-dimensionaliza- tion leads to the equation of motion as follows: Assuming specularly reflecting surfaces and a uniform radius of curvature pc for panels in the thermally deformed configuration, the expression for the generalized force was obtained as [8]: Thermal Deflection Analysis Let us study the uncontrolled librational dynamics of the satellite in the presence of solar heating. The study is initiated with an evaluation of the temperature gradient across the appendage due to solar heating, the associated deformation and resulting solar torque. The panels are assumed to be of a single homogeneous material. Since the estimates of heating ‘time constant’ are much smaller than the orbital period, a quasisteady analysis is undertaken. The differential equation governing the temperature variations across the panel thickness can be written as (Fig. 2) The analysis leads to the following temperature difference: As shown by Modi & Kumar [7] this expression can be approximated, to a fairly high degree of accuracy as: which in turn leads to the following dimensionless curvature as On substituting for yc from (3) into (1) and carrying out the necessary algebraic manipulation, the equation of librational motion takes the form:
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