On the apsidal limits of a rolling missile
Authors:
P. C. Rath and A. V. Namboodiri
Journal:
Quart. Appl. Math. 36 (1978), 1-17
DOI:
https://doi.org/10.1090/qam/99641
MathSciNet review:
QAM99641
Full-text PDF Free Access
Abstract |
References |
Additional Information
Abstract: It is proved that a rolling missile whose initial angular oscillations are nonlinear will have the same librations as its equivalent common top provided that $q > 0$ and ${Z_1} + {Z_4} \le - 2$ where $q$ is certain aerodynamic parameter contained in the nonlinear overturning moment of the missile and ${Z_1}$, ${Z_4}$ are respectively the least negative and the largest positive zeros of a certain quartic polynomial.
- Paul F. Byrd and Morris D. Friedman, Handbook of elliptic integrals for engineers and scientists, Die Grundlehren der mathematischen Wissenschaften, Band 67, Springer-Verlag, New York-Heidelberg, 1971. Second edition, revised. MR 0277773
- J. B. Diaz and F. T. Metcalf, Upper and lower bounds for the apsidal angle in the theory of the spherical pendulum, Proc. 4th U.S. Nat. Congr. Appl. Mech. (Univ. California, Berkeley, Calif., 1962) Amer. Soc. Mech. Engrs., New York, 1962, pp. 127–135. MR 0150998
- J. B. Diaz and F. T. Metcalf, Upper and lower bounds for the apsidal angle in the theory of the heavy symmetrical top, Arch. Rational Mech. Anal. 16 (1964), 214–229. MR 162387, DOI https://doi.org/10.1007/BF00250645
R. H. Fowler and C. N. H. Lock, The aerodynamics of a spinning shell II, Phil. Trans. Roy. Soc. London A 222, 227 (1922)
J. Hadamard, Sur la precession dans le mouvement d’un corps pesant de revolution fixé par un point de son axe, Bull. Sci. Math. 19, 228–230 (1895)
G. Halphen, Traité des functions elliptiques, vol. 2, Paris, Gauthier-Villars, 1888, p. 128
- Walter Kohn, Contour integration in the theory of the spherical pendulum and the heavy symmetrical top, Trans. Amer. Math. Soc. 59 (1946), 107–131. MR 15940, DOI https://doi.org/10.1090/S0002-9947-1946-0015940-7
P. C. Rath and A. V. Namboodiri, On the Lock-Fowler model of a spinning shell, Indian J. Pure Appl. Math. 5, 396–418 (1974)
P. C. Rath and A. V. Namboodiri, Librations of a Lock-Fowler missile, submitted to Memorial de L’Artillerie Francaise (Paris)
G. Salmon, A treatise on the higher plane curves, a reprint of the third edition of 1879, New York, G. E. Stechert and Co., 1934, p. 37
P. F. Byrd and M. D. Friedman, Handbook of elliptic integrals for engineers and scientists, 2d edition, Springer-Verlag, Berlin, Heidelberg, New York, 1971
J. B. Diaz and F. T. Metcalf, Upper and lower bounds for the apsidal angle in the theory of the spherical pendulum, in Proc. 4th U.S. Congress Appl. Mechanics, Univ. of Calif. Berkeley 1962, Vol 1, Amer. Soc. Mech. Engrs., New York (1962) pp. 127–135
J. B. Diaz and F. T. Metcalf, Upper and lower bounds for the apsidal angle in the theory of the heavy symmetrical top. Arch. Rat. Mech. Anal. 16, 214–229 (1964)
R. H. Fowler and C. N. H. Lock, The aerodynamics of a spinning shell II, Phil. Trans. Roy. Soc. London A 222, 227 (1922)
J. Hadamard, Sur la precession dans le mouvement d’un corps pesant de revolution fixé par un point de son axe, Bull. Sci. Math. 19, 228–230 (1895)
G. Halphen, Traité des functions elliptiques, vol. 2, Paris, Gauthier-Villars, 1888, p. 128
W. Kohn, Contour integration in the theory of the spherical pendulum and the heavy symmetrical top, Trans. Amer. Math. Soc. 59, 107–131 (1946)
P. C. Rath and A. V. Namboodiri, On the Lock-Fowler model of a spinning shell, Indian J. Pure Appl. Math. 5, 396–418 (1974)
P. C. Rath and A. V. Namboodiri, Librations of a Lock-Fowler missile, submitted to Memorial de L’Artillerie Francaise (Paris)
G. Salmon, A treatise on the higher plane curves, a reprint of the third edition of 1879, New York, G. E. Stechert and Co., 1934, p. 37
Additional Information
Article copyright:
© Copyright 1978
American Mathematical Society
