The dynamic stability of a uniform cantilever column under a tip-concentrated subtangential follower force is examined. The governing two-point boundary value problem is converted to an initial value problem. A simple numerical iterative scheme is followed to generate a load versus frequency curve (eigencurve) in order to study the critical and post-critical behavior of the columns subjected to a tip-concentrated follower force. For the load rotation parameter greater than 1 2 , the coalesce frequency and the corresponding critical load are obtained. The deformed configurations of cantilever columns are generated for different load rotation parameters. The details of the critical load parameter, tip angle and tip coordinates of the columns for the specified load rotation parameter are presented. The critical load parameter increases with the load rotation parameter.
In the history of space, for the first time an operational US communications satellite Iridium 33, in low-Earth orbit was struck and destroyed by the collision of a long defunct Russian communications satellite COSMOS 2251 on 10 th February 2010. It is necessary to understand the circumstances of this collision for avoiding similar incidents in the future. In this direction a detailed conjunction analysis of all space objects is essential. Since a large number of objects are orbiting in space, it is very difficult to find out the close approach for all objects with simulations. Hence, a study related to the prefiltering of close approaches between space objects using analytical techniques is carried out in this paper. It is found that the presented methodology with prefiltering techniques is effective in reducing the number of objects for simulations.
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