Spherical Harmonic Functions for Expression of Polyhedral Vibration of a Spherical Drop

Yoji Arai¹, Ken Adachi¹, and Ryuji Takaki²

¹University of Electro-Communications, Chofu, Tokyo 182, Japan
²Tokyo University of Agriculture and Technology, Fuchu, Tokyo 183, Japan

(Received December 24, 1990; Accepted April 15, 1991)

Keywords: Spherical Drop, Polyhedron, Vibration, Spherical Harmonic Function

Abstract. Instantaneous shapes of vibrating spherical drop are expressed by the spherical harmonic functions (abbreviated as SHF). Axisymmetric mode and the tetrahedral mode are expressed by a single SHF Observed shapes of drops in axisymmetric vibration were shown to coinside with SHF On the other hand, vibrations with the other regular-polyhedral mode are shown to be expressed by superpositions of several axisymmetric SHFs with their axes tilted by certain angles.