Lyubimov V.V.
Estimated probability of capture into resonance during the descent оf a rigid body with variable inertia asymmetry in the atmospere
During the descent in the atmosphere of an asymmetric rigid body possible implementation of a long resonance. Long resonance leads to a transition from rotational motion of the rigid body to oscillatory (implemented capture into resonance). The passage through the resonance is observed at short-term coincidence of frequencies of the system, not accompanied by an increase in the angle of attack. Initial conditions leading to the capture and passage through resonance, mixed on the separatrix randomly [1]. To calculate the probability of capture into resonance traditionally used the expression [2]. Solves the problem of estimating the probability of capture into resonance at atmospheric descent rigid body with variable inertia and constant aerodynamic asymmetries.
References
1. Lifshitz I.M., Sluckin A.A., Nabutovsky V.M. O yavlenii rasseyaniya zaryazhennyih kvazichastits na osobyih tochkah v p – prostranstve // Dokladyi AN SSSR. 1961. T.137. № 3. pp. 553-556.
2. Neishtadt A.I. Prohozhdenie cherez separatrisu v rezonansnoy zadache s medlenno izmenyayuschimsya parametrom // Prikladnaya matematika i mehanika. 1975. T.39. pp. 621-633.
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