Instability of a whirling conducting rod in the presence of a magnetic field. Application to the problem of space tethers

Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005

Volumn 6 A, Issue , 2005, Pages 35-44

  Valverde, J ^a   Van Der Heijden, G ^b  

^a UNIVERSITY OF SEVILLE   (Spain)

^b UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

AEROSPACE APPLICATIONS; BOUNDARY CONDITIONS; ELASTIC MODULI; ELECTRODYNAMICS; MAGNETIC FIELDS; ROTATION;

ELASTIC STRUCTURES; HELICAL POST-BUCKLING SOLUTIONS; SPACE TETHERS; WHIRLING CONDUCTING RODS;

TETHERLINES;

EID: 33244468385     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/detc2005-84845     Document Type: Conference Paper

References (20)

1. Woodson, H.H. and Melcher, J.R., 1968. Electromechanical Dynamics, Part II: Fields, Forces, and Motion. John Wiley & Sons, New York.
2. Wolfe, P., 1983. "Equilibrium states of an elastic conductor in a magnetic field: A paradigm of bifurcation theory". Trans. Am. Math. Soc. 278, pp. 377-387.
3. Wolfe, P., 1985. "Rotating states of an elastic conductor", in: Physical Mathematics and Nonlinear Partial Differential Equations, J. Lightbourne and S. Rankin (eds), Dekker, New York.
4. Healey, T.J., 1990. "Large rotating states of a conducting elastic wire in a magnetic field: subtle symmetry and multiparameter bifurcation". J. Elasticity 24, pp. 211-227.
5. Wolfe, P., 1988. "Bifurcation theory of an elastic conducting rod in a magnetic field". Quart. J. Mech. Appl. Math., 41(2), pp. 265-279.
6. Beletsky, V.V. and Levin, E.M., 1993. Dynamics of Space Tether Systems. Advances in the Astronautical Sciences Volume 83, American Astronautical Society.
7. Krupa, M., Kuhn, A., Poth, W., Schagerl, M., Steindl, A., Steiner, W., Troger, H. and Wiedermann, G., 2000. "Tethered satellite systems: A new concept of space flight". Eur. J. Mech. A Solids 19, pp. 145-164.
8. Ziegler, S.W. and Cartmell, M.P., 2001. "Using motorized tethers for payload orbital transfer". Journal of Spacecraft and Rockets 38, pp. 904-913.
9. Valverde, J., Escalona, J.L., Mayo, J. and Domínguez, J., 2003. "Dynamic analysis of a light structure in outer space: Short Electrodynamic Tether". Multibody System Dynamics 10(1), pp. 125-146.
10. Valverde, J., Escalona, J.L., Domínguez, J. and Champneys, A.R. "Stability and bifurcation analysis of the short electrodynamic tether, a geometrically nonlinear approach", submitted to Journal of Nonlinear Science.
11. Valverde, J., Escalona, J.L., Freire, E. and Domínguez, J., in the press. "Stability and bifurcation analysis of a geometrically nonlinear orthotropic Jeffcott model with internal damping". Nonlinear Dynamics.
12. Cosmo, M.L. and Lorenzini, E.C., 1997. Tethers in Space Handbook, 3rd edition. Smithsonian Astrophisical Observatory (NASA Marshall Space Flight Center).
13. Antman, S.S., 1995. Nonlinear Problems of Elasticity. Springer-Verlag, Berlin.
14. Coleman, B.D., Dill, E.H., Lembo, M.,Lu, Z. and Tobias,I., 1993. "On the dynamics of rods in the theory of Kirchhoff and Clebsch". Arch. Rat. Mech. Anal. 121, pp. 339-359.
15. Jackson, J.D., 1975. Classical Electrodynamics, 2nd edition. John Wiley & Sons, New York.
16. Doedel, E.J., Champneys, A.R., Fairgrieve, T.R., Kuznetsov, Yu.A., Sandstede, B. and Wang, X.J., 1997. AUTO97: Continuation and bifurcation software for ordinary differential equations (available by anonymous ftp from ftp.cs.concordia.ca/pub/doedel/auto).
17. Tyc, G., Han, R.P.S., Vigneron, F.R., Jablonski, A.M., Modi, V.J. and Misra, A.K., 1993. "Dynamics and stability of a spinning tethered spacecraft with flexible appendages". Advances in the Astronautical Sciences 85(1), pp. 877-896.
18. Vigneron, F.R., Jablonski, A.M., Chandrashaker, R. and Tyc, G., 1997. "Damped gyroscopic modes of spinning tethered space vehicles with flexible booms". Journal of Spacecraft and Rockets 34(5), pp. 662-669.
19. Scheibel, T., Parthasarathy, R., Sawicki, G., Lin, X.M., Jaeger, H. and Lindquist, S.L., 2003. "Conducting nanowires built by controlled self-assembly of amyloid fibers and selective metal deposition". Proc. Nat. Acad. Sci. USA 100, pp. 4527-4532.
20. Maiya, B.G. and Ramasarma, T., 2001. "DNA, a molecular wire or not - The debate continues". Current Science 80(12), pp. 1523-1530.