6533b822fe1ef96bd127cbaf

RESEARCH PRODUCT

Stability analysis of an electromagnetically levitated sphere

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We present a combined numerical and analytical approach to analyze the static and dynamic stabilities of an electromagnetically levitated spherical body depending on the ac frequency and the configuration of a three-dimensional (3D) coil made of thin winding which is modeled by linear current filaments. First, we calculate numerically the magnetic vector potential in grid points on the surface of the sphere and then use Legendre and fast Fourier transforms to find the expansion of the magnetic field in terms of spherical harmonics. Second, we employ a previously developed gauge transformation to solve analytically the 3D electromagnetic problem in terms of the numerically obtained expansion coefficients. Using this solution, we obtain the electromagnetic reaction force due to both a small displacement of the sphere from its equilibrium position and its velocity of motion which are defined by symmetric stiffness and damping matrices, respectively. Eigenvalues and eigenvectors of the stiffness matrix yield ...