In this paper, a minimum and near-minimum time optimal control laws are developed and compared for a rigid space platform with flexible links during an orientating maneuver with large angle of rotation. The control commands are considered as typical bang-bang with multiple symmetrical switches, the time optimal control solution for the rigid-body mode is obtained as a bang-bang function and app...

In this paper, some results are provided for minimum time roll about velocity vector maneuvering with thrust-vectoring and aerodynamic control in effect. The mathematical model for attitude motions of the aircraft is developed. First order necessary conditions for optimality using Pontryagen principle is applied, and the existence of an extreme family of solutions for the maneuver is shown. Mul...

1389 with u(w; s) = jwj1u(^ w; s) where ^ w = w=jwj1. For any w 2 R 2 and s 2 f0; 1g; jz(w;s)j 1 6jwj 1. We now turn our attention to signals w(k) 2 l n 1 and w(t) 2 L n 1 , and to distinguish them from vectors in R n we will use boldface type.

Given a set of n disjoint line segments in the plane, we show that it is always possible to form a spanning tree of the endpoints of the segments, such that each line segment is an edge of the tree and the tree has no crossing edges. We also show that the maximum degree of a node in the minimum weight spanning tree formed by these line segments is seven, and that there exists a set of line segm...

In this paper, we investigate the spatial distribution of solar flares in the northern and southern hemisphere of the Sun that occurred during the period 1996 to 2003. This period of investigation includes the ascending phase, the maximum and part of descending phase of solar cycle 23. It is revealed that the flare activity during this cycle is low compared to previous solar cycle, indicating t...