Application of the Krylov-Bogoliubov-Mitropolski Technique for a Rotating Heavy Solid under the Influence of a Gyrostatic Moment

被引：30

作者：

Amer, T. S. ^{[1
,2
]}

Ismail, A. I. ^{[1
]}

Amer, W. S. ^{[3
]}

机构：

[1] Tanta Univ, Dept Math, Fac Sci, Tanta 31527, Egypt

[2] Taif Univ, Al Khurmah Branch, Dept Math, Fac Sci & Educ, At Taif, Saudi Arabia

[3] Menoufia Univ, Dept Math, Fac Sci, Shebin El Koum, Egypt

来源：

JOURNAL OF AEROSPACE ENGINEERING | 2012年 / 25卷 / 03期

关键词：

Euler's equations; Periodic solutions; Nonlinear oscillations; Perturbation methods; FIXED-POINT; RIGID-BODY; MOTION;

D O I：

10.1061/(ASCE)AS.1943-5525.0000117

中图分类号：

V [航空、航天];

学科分类号：

08 ; 0825 ;

摘要：

The rotational motion of a heavy solid about a fixed point in the presence of a gyrostatic moment vector is investigated in this paper. It is supposed that the body is rapidly spinning about the major or the minor principle axis of the ellipsoid of inertia. The Krylov-Bogoliubov-Mitropolski technique is modified to obtain the periodic solutions of the equations of motion of the body with nonzero basic amplitude. These solutions are performed by computer codes to get their graphical representations. The result of this study was compared with similar previous works. DOI: 10.1061/(ASCE)AS.1943-5525.0000117. (C) 2012 American Society of Civil Engineers.

引用

页码：421 / 430

页数：10

共 19 条

[1]

Arkhangel'skii I. A., 1975, C MATH SOC J BOLYAI, P27

[2]

Bakhmutskii V. F., 1961, IZV AKAD NAUK SSSR, V3, P84

[3]

Bogoliubov N.N., 1961, Asymptotic Methods in the Theory of Non-linear Oscillations

[4] New control laws for stabilization of a rigid body motion using rotors system [J].

El-Gohary, Awad .

MECHANICS RESEARCH COMMUNICATIONS, 2006, 33 (06) :818-829

[5] LIMITING CASE FOR THE MOTION OF A RIGID-BODY ABOUT A FIXED-POINT IN THE NEWTONIAN FORCE-FIELD [J].

ELBARKI, FA ;

ISMAIL, AI .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1995, 75 (11) :821-829

[6]

Ismail AI, 1996, Z FLUGWISS WELTRAUM, V20, P205

[7] Periodic solutions of equations of motion of a heavy solid applying Krylov-Bogoliubov-Mitropolski method [J].

Ismail, AI .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 114 (02) :345-359

[8] The motion of fast spinning rigid body about a fixed point with definite natural frequency [J].

Ismail, AI .

AEROSPACE SCIENCE AND TECHNOLOGY, 1997, 1 (03) :183-190

[9]

Iu A., 1963, PMM-J APPL MATH MEC, V27, P1314

[10]

Iu A., 1963, PMM-J APPL MATH MEC, V272, P551, DOI DOI 10.1016/0021-8928(63)90023-6

← 1 2 →