Novel Finite Particle Method for Gyrodynamics Analysis.

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  • LEE Hsing-Juin
    Department of Mechanical Engineering, National Chung-Hsing University

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Abstract

Traditionally, Euler’s equations are commonly employed for the analyses of interesting gyrodynamics problems. Nevertheless, they generally give no idea how these complicated gyroscopic forces are mutually interacting. Thus, we may risk missing some insights regarding working forces. Therefore, in this study, we present a so-called “finite particle method, ” which simulates a gyroscope by a small number of dynamically equivalent particles (usually 2 to 8 only) rigidly connected. This method largely degenerates complicated 3-D gyrodynamics to a particle dynamics problem in a rotating frame. The finite particle method has elegantly demonstrated its validity by successfully deriving the same steady gyrodynamics equations as that derived from Euler’s approach, yet only in amazingly minimal steps for some cases. Surprisingly enough, by this method, one can swiftly understand some delicate gyrodynamics phenomena more deeply by merely inspecting centripetal and Coriolis forces particle by particle, without even knowing what angular momentum is. In short, this finite particle method is characterized by its simpler concept, succinct derivation, and possibly insightful understanding of intrinsic force interactions for some gyrodynamics problems as demonstrated in the retrograding phenomenon of disk-shaped satellites and other examples.

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