Research Papers

To the Problem of a Passive Levitation of Bodies in Physical Fields

[+] Author and Article Information
G. G. Denisov, V. V. Novikov, A. E. Fedorov

 Nizhniy Novgorod State University, 23 Gagarin Avenue, Nizhniy Novgorod 603022, Russian Federation

J. Appl. Mech 77(3), 031017 (Feb 24, 2010) (6 pages) doi:10.1115/1.4000384 History: Received January 05, 2007; Revised August 14, 2009; Published February 24, 2010; Online February 24, 2010

A possibility of levitation of a body carrying a point electrical charge in the field of a fixed point charge of the same sign is shown. Stabilization of an unstable equilibrium, when gravity is compensated by Coulomb’s force, is realized using gyroscopic forces generated due to the rotation of the body. A finite range of angular velocity corresponds to conservative stability of the levitating body. It is shown that dissipative and circulation forces introduced into consideration simultaneously can improve the stability of the system to asymptotic. Dependence of the domain of attraction of stable equilibrium on parameters of the system is studied numerically.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

A symmetric rigid body with an electric charge q rotates with angular speed φ̇ in a field of an identical fixed electrical charge q located in the origin of the coordinate system. Radius vectors r and r1 define the position of the center of mass of the levitating body and position of the charge connected with it correspondingly. (a) Equilibrium state of the system and (b) nonequilibrium state of the system.

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Figure 2

A system of angular coordinates of the symmetry axis of levitating body

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Figure 3

Dependence of parameter H, characterizing the gyroscopic properties of a body on oscillation frequency and p: (a) under condition of χ−δ2>0 and (b) under condition of χ−δ2<0. The interval [Hmin,Hmax] is the region of stability.

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Figure 4

The regions of stability of the parameter plane for different H from interval 5≤H≤10 with step 1: (a) with condition of χ−δ2>0 and (b) with χ−δ2<0

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Figure 5

The picture of D-partitioning of a plane of circulation forces coefficients κ1,κ2. Quadrilateral abcd is the region of asymptotic stability.

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Figure 6

The deviation of full energy E of the system from initial value E0 during numerical integration. It is used for the control of calculation accuracy.

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Figure 7

Trajectory of motion of the center of mass of the body in linear (dotted line) and nonlinear cases with the parameters from the region of stability

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Figure 8

The domain of attraction of a stable equilibrium (a) in the plane of R=x2+y2, z, and (b) in the plane of α, z

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Figure 9

Dependence of the sizes of domain of attraction on parameters of the system at H=6 in the case of (a) δ>0 and (b) δ<0 correspondingly



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