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Stability Analysis of a Rigid Body with Attached Geometrically Nonlinear Rod by the Energy-Momentum Method
| Content Provider | Semantic Scholar |
|---|---|
| Abstract | This paper applies the energy-momentum method to the problem of nonlin-ear stability of relative equilibria of a rigid body with attached Hexible appendage in a uniformly rotating state. The appendage is modeled as a geometrically exacL rod which allows for finite bending, shearing and twist in Lhree dimensions. Ap-r-'" plication of the energy-momentum method to this example depends crucially on a. special choice of variables in terms of which the second variation block diagonal-izes into blocks associated with rigid body modes and internal vibration modes respectively. The ·analysis yields a nonlinear stability result which states that relative equilibria are nonlinearly stable provided that; (i) the angular velocity is bounded above by the square root of the minimum eigenvalue of an associated linear operator and, (ii) the whole assemblage is rotating about the minimum axis of inertia. §1. Introduction This paper discusses the application of the energy-momentum method to the case of a rotaLing rigid body with an attached, flexible appendage. The model for the appendage we have chosen is referred La a a geometrically exacL rod model andported by AFOSR contract nwnbcrs 2.DJA-544 and 2.DJA-771 with Stanrord Univcrsity. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://authors.library.caltech.edu/19972/1/SiPoMa1989.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
