On the Stability of the Regular Precession of an Asymmetric Gyroscope at a Second-order Resonance

被引：0
作者：
Anatoly P. Markeev
机构：
[1] Ishlinsky Institute for Problems in Mechanics RAS,
[2] Moscow Aviation Institute (National Research University),undefined
来源：
Regular and Chaotic Dynamics | 2019年 / 24卷
关键词：
rigid body; precession; stability; 70E17; 70E50; 70H14;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The motion of a rigid body about a fixed point in a homogeneous gravitational field is investigated. The body is not dynamically symmetric and its center of gravity lies on the perpendicular, raised from the fixed point, to one of the circular sections of an ellipsoid of inertia. A body with such mass geometry may precess regularly about a nonvertical axis (Grioli’s precession). The problem of the orbital stability of this precession is solved for critical cases of second-order resonance, when terms higher than degree four in the series expansion of the Hamiltonian of the perturbed motion should be taken into account.
引用
收藏
页码：502 / 510
页数：8
相关论文
共 14 条
[1]  
Grioli G(1947)Esistenza e determinazione delle precessioni regolari dinamicamente possibili per un solido pesante asimmetrico Ann. Mat. Pura Appl. (4) 26 271-281
[2]  
Markeyev A P(2003)The Stability of the Grioli Precession J. Appl. Math. Mech. 67 497-510
[3]  
Gulyaev M P(1958)On Dynamically Possible Regular Precessions of Rigid Body with One Fixed Point Tr. Sekt. Mat. Mekh. Akad. Nauk Kaz. SSR 1 202-208
[4]  
Gulyaev M P(1958)On Circular Cross-Sections of Mutual Ellipsoids of Inertia Tr. Sekt. Mat. Mekh. Akad. Nauk Kaz. SSR 1 175-193
[5]  
Grioli G(1949)Questioni di stabilita reguardanti le precessioni regolari del solido pesante asimmetrico Ann. Sc. Norm. Super. Pisa. Ser. 3 1 43-71
[6]  
Tkhai V N(2000)The Stability of Regular Grioli Precessions J. Appl. Math. Mech. 64 811-819
[7]  
Markeyev A P(2002)An Algorithm for Normalizing Hamiltonian Systems in the Problem of the Orbital Stability of Periodic Motions J. Appl. Math. Mech. 66 889-896
[8]  
Markeev A P(2002)On the Stability of the Regular Precession of an Asymmetric Gyroscope Dokl. Phys. 47 833-837
[9]  
Markeev A P(2018)On the Stability of the Regular Grioli Precession in One Particular Case J. Appl. Math. Mech. 53 S1-S14
[10]  
Markeev A P(2018)On Stability of Regular Precession of an Asymmetrical Gyroscope in a Critical Case of the Fourth-Order Resonance Dokl. Phys. 63 297-301
12