Solar radiation can induce circumferential temperature gradients and thermoelastic bending moments in lightweight spacecraft appendages. For spinning spacecraft, this thermal excitation is periodically modulated by spin motion and may amplify flexible response when the modulation frequency approaches a structural frequency. This study investigates the spin-modulated thermoelastic response of a spacecraft with a circular thin-walled flexible appendage under attitude-dependent solar radiation. A reduced-order rigid-flexible-thermal model is formulated by coupling rigid-body attitude motion, assumed-mode appendage deformation, first-harmonic circumferential temperature perturbations, and the resulting generalised thermoelastic bending moment. Long-time simulations, spin-period response sampling, degraded-model comparisons and modal energy/work diagnostics are used to identify the dominant response mechanism. The results show that the post-transient flexible response is governed mainly by spin rate, while the initial solar-incidence angle modifies the local response classification in the sampled high-spin region. Representative high-spin loss-of-admissibility cases lie near the first bending-frequency region, where the retained structural energy and positive thermoelastic work input are concentrated mainly in the first bending mode. Removing deformation-dependent solar-incidence feedback does not eliminate these cases, whereas suppressing thermoelastic bending does. Thus, spin-modulated thermoelastic bending is the essential pathway by which attitude-dependent solar radiation amplifies appendage response.
This paper presents the stability of resonant rotation of a symmetric gyrostat under third- and fourth-order resonances, whose center of mass moves in an elliptic orbit in a central Newtonian gravitational field. The resonant rotation is a special planar periodic motion of the gyrostat about its center of mass, i. e., the body performs one rotation in absolute space during two orbital revolutions of its center of mass. The equations of motion of the gyrostat are derived as a periodic Hamiltonian system with three degrees of freedom and a constructive algorithm based on a symplectic map is used to calculate the coefficients of the normalized Hamiltonian. By analyzing the Floquet multipliers of the linearized equations of perturbed motion, the unstable region of the resonant rotation and the region of stability in the first-order approximation are determined in the dimensionless parameter plane. In addition, the third- and fourth-order resonances are obtained in the linear stability region and further nonlinear stability analysis is performed in the third- and fourth-order resonant cases.
28 November 2024 in Communications in Nonlinear Science and Numerical Simulation
Online fixed-wing guidance can generate an attitude command without supplying the angular motion required by a moving-reference torque controller. For the selected governed attitude, Direct realization supplies compatible nominal angular velocity and acceleration without replacing the attitude command by an additional active filter reference. The known dynamics of the existing governor close nominal angular acceleration at the first derivative of the raw command. The adopted guidance supplies that derivative using desired position data only through acceleration, without future samples or an additional active attitude filter. On the smooth strict-interior branch, the compatible triplet and adopted torque law define an invariant nominal moving manifold with local exponential decay. Kinematic and momentum residuals describe physical departure and enter a conditional local rotational error bound. Matched aircraft simulations examine how nominal closure translates into physical tracking and actuator demand relative to a fixed tuning of the specified attitude filter, termed the Performance-Tuned Baseline. In the combined wind and body moment case, this baseline has a root-mean-square (RMS) error relative to the attitude command of 0.04543°, versus 0.12465° for Direct. The corresponding peak component surface rates over the full run are 9.7377 and 4.3913 deg/s. Both peaks occur during startup under common initialization. The comparisons distinguish nominal interface closure from physical performance and show trade-offs between tracking and actuation.
This paper deals with periodic motions and their stability of a flexible connected two-body system with respect to its center of mass in a central Newtonian gravitational field on an elliptical orbit. Equations of motion are derived in a Hamiltonian form and two periodic solutions as well as the necessary conditions for their existence are acquired. By analyzing linearized equations of perturbed motions, Lyapunov instability domains and domains of stability in the first approximation are obtained. In addition, the third and fourth order resonances are investigated in linear stability domains. A constructive algorithm based on a symplectic map is used to calculate the coeffcients of the normalized Hamiltonian. Then a nonlinear stability analysis for two periodic solutions is performed in the third and fourth order resonance cases as well as in the nonresonance case.