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Approximate Solution to the Angular Speeds of a Nearly-Symmetric Mass-Varying Cylindrical Body

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Abstract

This paper examines the rotational motion of a nearly axisymmetric rocket type system with uniform burn of its propellant. The asymmetry comes from a slight difference in the transverse principal moments of inertia of the system, which then results in a set of nonlinear equations of motion even when no external torque is applied to the system. It is often difficult, or even impossible, to generate analytic solutions for such equations; closed form solutions are even more difficult to obtain. In this paper, a perturbation-based approach is employed to linearize the equations of motion and generate analytic solutions. The solutions for the variables of transverse motion are analytic and a closed-form solution to the spin rate is suggested. The solutions are presented in a compact form that permits rapid computation. The approximate solutions are then applied to the torque-free motion of a typical solid rocket system and the results are found to agree with those obtained from the numerical solution of the full non-linear equations of motion of the mass varying system.

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of California, Davis, CA, USA

    Angadh Nanjangud & Fidelis Eke

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  1. Angadh Nanjangud
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  2. Fidelis Eke
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Correspondence to Angadh Nanjangud.

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Nanjangud, A., Eke, F. Approximate Solution to the Angular Speeds of a Nearly-Symmetric Mass-Varying Cylindrical Body. J of Astronaut Sci 64, 99–117 (2017). https://doi.org/10.1007/s40295-016-0099-8

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  • DOI: https://doi.org/10.1007/s40295-016-0099-8

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