Abstract
A nonlinear differential equation representing the initial nutational vibrations of a spinning projectile in the presence of a nonlinear Magnus moment has been approximated by a perturbed Duffing’s equation and the quantitative and qualitative agreement of the approximation brought out. Then the combined motion in nutation and precession has been examined and sufficient conditions for the Magnus instability of the normal motion establishedvia Lyapunov’s second method.
Similar content being viewed by others
References
Bogoliubov N N & Mitropolsky Y A 1961Asymptotic methods in the theory of nonlinear oscillation (Delhi: Hindustan Publishing Corpn.)
Efimov N V & Rozendorn E R 1975Linear algebra and multidimensional geometry (Moscow: Mir Publishers)
Fowler R H & Lock C N H 1922Philos. Trans. R. Soc. A 222 227
La Salle J & Lefschetz S 1961Stability by Liapunov’s direct method (New York: Academic Press)
Rath P C & Sharma K C 1976Indian J. Pure Appl. Math. 7 387
Rath P C & Sharma S M 1981Aeronaut. Q. London 23 228
Sharma S M 1975J. Armt. Studies 11 18
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sharma, S.M. On the instability of a spinning projectile due to a nonlinear Magnus moment. Proc. Indian Acad. Sci. (Engg. Sci.) 4, 449–459 (1981). https://doi.org/10.1007/BF02896346
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02896346