Asymmetrical chattering arc in vertical plane flight

The asymmetrical chattering are of a winged space vehicle in the vertical plane reentry flight has been studied. With the use of dimensionless variables, we need only two parameters to specify the aerodynamic characteristics of the vehicle, one is the ballistic coefficient and the other is the maximum lift-to-drag ratio. The control variable is the normalized lift coefficient (NLC), the ratio of the lift coefficient and the lift coefficient at the maximum lift-to-drag ratio. The chattering flight happens when the NLC switches rapidly between its maximum and minimum values. We use the chattering control on the NLC to obtain maximum drag, or say, maximum deceleration. The asymmetrical chattering are will be existing when the maximum and minimum NLCs have different absolute values. We started the study of the asymmetrical chattering from an example of basic dynamical system. It is found that a singular are can be replaced by either a symmetrical or an asymmetrical chattering are. The net effects on the lift and drag will be the weighted sums of the first and second orders of the maximum and minimum NLCs, respectively. The weighting factor is the percentage of acting time. A typical asymmetrical chattering reentry flight has the characteristics of maximum deceleration and phugoid oscillation. (C) 2000 Elsevier Science Ltd. All rights reserved.