Optimal control of the spatial motion of a viscoelastic rod

نویسندگان

  • Thomas I. Seidman
  • Stuart S. Antman
چکیده

1. Introduction We consider a model [1] of a nonlinearly viscoelastic rod moving in 3-dimensional space, taking into account not only longitudinal and transverse motions, but also shear and torsional motion: One may visualize this, dis-cretized, as a chain of hard vertebrae connected by a viscous springy material. This paper is related to the forthcoming [3] much as [9] was related to [2]. The papers [2] and [9] treat the purely longitudinal motion of a straight rod. As in [9], we show that the attainment of optimality for certain control problems is intimately related to the considerations involved in showing the existence of solutions , in particular, to the requirement that a subsequential limit of solutions to some approximating problems should be solutions of a desired limit problem.

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تاریخ انتشار 2010