The problem of optimal control of a Chaplygin ball by internal rotors

被引：12
|
作者：
Bolotin, Sergey [1 ,2 ]
机构：
[1] Univ Wisconsin, Madison, WI 53706 USA
[2] Russian Acad Sci, VA Steklov Math Inst, Moscow 119991, Russia
来源：
REGULAR & CHAOTIC DYNAMICS | 2012年 / 17卷 / 06期
关键词：
nonholonomic constraint; vaconomic mechanics; optimal control; maximum principle; Hamiltonian; NONINTEGRABLE CONSTRAINTS; SYSTEMS; SPHERE;
D O I：
10.1134/S156035471206007X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the problem of optimal control of a Chaplygin ball on a plane by means of 3 internal rotors. Using Pontryagin maximum principle, the equations of extremals are reduced to Hamiltonian equations in group variables. For a spherically symmetric ball, the solutions can be expressed in by elliptic functions.
引用
收藏
页码：559 / 570
页数：12
相关论文
共 50 条
  • [1] The problem of optimal control of a Chaplygin ball by internal rotors
    Sergey Bolotin
    [J]. Regular and Chaotic Dynamics, 2012, 17 : 559 - 570
  • [2] How to control the Chaplygin ball using rotors. II
    Alexey V. Borisov
    Alexander A. Kilin
    Ivan S. Mamaev
    [J]. Regular and Chaotic Dynamics, 2013, 18 : 144 - 158
  • [3] How to control the Chaplygin ball using rotors. II
    Borisov, Alexey V.
    Kilin, Alexander A.
    Mamaev, Ivan S.
    [J]. REGULAR & CHAOTIC DYNAMICS, 2013, 18 (1-2): : 144 - 158
  • [4] On the chaplygin problem of the rolling of a ball
    Tsyganov, A. V.
    [J]. MATHEMATICAL NOTES, 2013, 94 (3-4) : 599 - 602
  • [5] On the chaplygin problem of the rolling of a ball
    A. V. Tsyganov
    [J]. Mathematical Notes, 2013, 94 : 599 - 602
  • [6] The problem of drift and recurrence for the rolling Chaplygin ball
    Alexey V. Borisov
    Alexander A. Kilin
    Ivan S. Mamaev
    [J]. Regular and Chaotic Dynamics, 2013, 18 : 832 - 859
  • [7] Chaplygin's Ball Rolling Problem Is Hamiltonian
    A. V. Borisov
    I. S. Mamaev
    [J]. Mathematical Notes, 2001, 70 : 720 - 723
  • [8] The problem of drift and recurrence for the rolling Chaplygin ball
    Borisov, Alexey V.
    Kilin, Alexander A.
    Mamaev, Ivan S.
    [J]. REGULAR & CHAOTIC DYNAMICS, 2013, 18 (06): : 832 - 859
  • [9] Chaplygin's ball rolling problem is Hamiltonian
    Borisov, AV
    Mamaev, IS
    [J]. MATHEMATICAL NOTES, 2001, 70 (5-6) : 720 - 723
  • [10] How to control Chaplygin’s sphere using rotors
    Alexey V. Borisov
    Alexander A. Kilin
    Ivan S. Mamaev
    [J]. Regular and Chaotic Dynamics, 2012, 17 : 258 - 272
12345