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
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
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.

Grahic Jump Location
Figure 2

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

Grahic Jump Location
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.

Grahic Jump Location
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

Grahic Jump Location
Figure 5

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

Grahic Jump Location
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.

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In