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A nonlinear oscillator analog of rigid body dynamics

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Abstract

A rigorously valid nonlinear oscillator analog of the torque-free rotational dynamics of a general rigid body is presented. The analog consists of threeuncoupled nonlinear oscillators, the motion of each being governed by a second order nonlinear ordinary differential equation of the Duffing type. The nonlinear oscillator analog and three associated phase planes, as established herein, provide a new basis for analysis and visualization of rigid body dynamics. The phase planes are particularly useful in providing complete visibility of the motion's limiting cases and stability properties.

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Authors and Affiliations

  1. Dept. of Aerospace Engineering and Engineering Physics, Univ. of Virginia, Charlottesville, Va., U.S.A.

    John L. Junkins & Ira D. Jacobson

  2. Research Laboratories for the Engineering Sciences, Univ. of Virginia, Charlottesville, Va., U.S.A.

    Jeffrey N. Blanton

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  1. John L. Junkins
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  2. Ira D. Jacobson
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  3. Jeffrey N. Blanton
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Junkins, J.L., Jacobson, I.D. & Blanton, J.N. A nonlinear oscillator analog of rigid body dynamics. Celestial Mechanics 7, 398–407 (1973). https://doi.org/10.1007/BF01227506

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  • DOI: https://doi.org/10.1007/BF01227506

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