Dynamic modeling and stability analysis of a flexible spinning missile under thrust

Abstract

The general equations of motion of a flexible spinning missile under thrust in the powered flight phase are established and the stability of the motion of the missile is analyzed. The spinning missile is approximated to the unconstrained flexible rotor. Moreover, the thrust in the powered flight phase is deemed as a follower load when the factors of gyroscopic effect, aeroelastic effect, and axial force are considered under the mean axis condition. The equations of motion and stability of the flexible spinning missile in the powered flight phase are then deduced. The stability and dynamic response of the flexible spinning missile under thrust is analyzed through numerical calculation. Calculation results show that thrust, spinning speed, and dynamic pressure exert different influences on the stability of the spinning missile. These factors should be considered and analyzed comprehensively.

Research on dynamic stability of rolling missiles employing direct/aerodynamic force compound control

“…17. According to that the spinning missile can be simplified to the flexible rotor with no constraints, Xu et al 18 studied the dynamic response and stability of a flexible spinning missile under thrust.…”

Stability of a flexible missile and asymptotics of the eigenvalues of fourth order boundary value problems

“…The boundary conditions, of the problems investigated in [4,6,7], are y (3) (0) = y (0) = 0 and y (3) (a) = y (a) = 0 (1.3) and their operator polynomial representation is (1.4) in the Hilbert space L 2 (0, a). Recently, Xu, Rong, Xiang, Pan and Yin [24], using numerical calculations, have investigated the dynamic response and stability of a rotating and flexible missile under thrust.…”

“…24 − γ 23 γ 14 = −(1 − i)μ 5 + 3 + i)g(0)μ3 + o(μ3 ), (6.2)γ 12 γ 23 − γ 22 γ 13 = (1 + i)μ 5 − 3 − i)g(0)μ 3 + o(μ 3 ), (6.3) γ 31 γ 42 − γ 32 γ 41 = (1 − i)μ 5 + 1 2 i G(a)μ 4 − 1 16 (1 + i) G 2 (a) + 12g(a) μ 3 + o(μ 3 ), (6.4)γ 31 γ 44 − γ 34 γ 41 = (1 + i)μ 5 + 1 2 i G(a)μ 4 − 1 16 (1 − i)(G 2 (a) + 12g(a)) + o(μ 3 ). (6.5)Therefore, it follows from (5.12) and (5.13) thatψ 1 (μ) = 2iμ 10 + 1 + i)G(a)μ 9 + 1 (a) + 12(g(0) + g(a))μ 8 + o(μ 8 ), (6.6) ψ 4 (μ) = 2iμ 10 − 1 − i)G(a)μ 9 + 1 (a) + 12(g(0) + g(a))μ 8 + o(μ 8 ).…”

Sensor placement and moving horizon state/parameter estimation for flexible hypersonic vehicles

“…To solve this problem, the flexible states that are difficult to be measured directly need to be provided for feedback. 9 Besides the flexible states, the natural frequencies of flexible modes 10 also have great influences on the dynamic response characteristics. With an inaccurate value of this parameter, the state estimation error could become large.…”