 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| A. V. Molodenkov, "On the solution of the Darboux problem," Mech. Solids. 42 (2), 167-176 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
2 |
Pages |
167-176 |
| Title |
On the solution of the Darboux problem |
| Author(s) |
A. V. Molodenkov (Institute for Problems in Precision Mechanics and Control, Rabochaya 24, Saratov, 410028, Russia, iptmuran@san.ru) |
| Abstract |
We consider the problem of determining the angular position of a rigid body in space from its known angular velocity and initial position (the Darboux problem) in quaternion setting. For an arbitrary angular velocity vector of the body, we present a solution based on Lappo-Danilevskii’s recursion relations [1]. New special cases of solvability of the Darboux problem in closed form are obtained. |
| References |
| 1. | I. A. Lappo-Danilevskii,
Application of Matrix Functions to the Theory of Linear Systems
of Ordinary Differential Equations
(Gostekhizdat, Moscow, 1957)
[in Russian]. |
| 2. | A. I. Lurie, Analytic Mechanics (Fizmatgiz, Moscow,
1961) [in Russian]. |
| 3. | V. N. Branets and I. P. Shmyglevskii, Application of
Quaternions to Rigid Body Orientation Problems (Nauka,
Moscow, 1973) [in Russian]. |
| 4. | P. K. Plotnikov and Yu. N. Chelnokov,
"Application of Quaternion Matrices in the Theory
of Finite Rotation of a Rigid Body,"
in Collection of Scientific and Methodological Papers in Theoretical Mechanics
(Vysshaya Shkola, Moscow, 1981),
No. 11, pp. 122-129
[in Russian]. |
| 5. | Yu. N. Chelnokov,
"Quaternions and Related Transformations in Dynamics
of a Symmetric Rigid Body. II,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 3-18 (1998)
[Mech. Solids (Engl. Transl.)]. |
| 6. | E. A. Ivanova,
"On One Approach to Solving the Darboux Problem,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 1, 45-52 (2000)
[Mech. Solids (Engl. Transl.)]. |
| 7. | V. I. Zubov, Analytic Dynamics of Gyro Systems
(Sudostroenie, Leningrad, 1970) [in Russian]. |
| 8. | V. I. Kalenova and V. M. Morozov, "On the Application of
Reducibility Methods to Problems of Dynamics of Gyro
Systems," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 1,
8-14 (1987) [Mech. Solids (Engl. Transl.)]. |
| 9. | V. M. Morozov and V. I. Kalenova,
Estimation and Control in Nonstationary Linear
Systems (Izd-vo MGU, Moscow, 1988) [in Russian]. |
| 10. | G. P. Sachkov and Yu. M. Kharlamov,
"On the Integrability of Kinematic Equations of Rotation,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 6, 11-15 (1991)
[Mech. Solids (Engl. Transl.)]. |
| 11. | Yu. N. Chelnokov,
"On Determining the Object Orientation in Rodrigues-Hamilton Parameters
from Its Angular Velocity,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 3, 11-20 (1977)
[Mech. Solids (Engl. Transl.)]. |
| 12. | P. K. Plotnikov,
Gyroscopic Measurement Systems
(Izd-vo Saratov Univ., Saratov, 1976)
[in Russian]. |
| 13. | N. P. Erugin,
"Reducible Systems,"
Trudy Mat. Inst. Steklov
13, 1-95 (1947)
[Proc. Steklov Inst. Math.]. |
|
| Received |
13 April 2004 |
| Link to Fulltext |
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