 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4760 |
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| A. P. Blinov, "On the motion of a mass point on a surface," Mech. Solids. 42 (1), 19-23 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
1 |
Pages |
19-23 |
| Title |
On the motion of a mass point on a surface |
| Author(s) |
A. P. Blinov (Timiryazev Moscow Agriculture Academy, Russian State Agricultural University, Timiryazevskaya 49, Moscow, 127550, Russia) |
| Abstract |
The motion of a mass point (particle) on a smooth surface in a potential force field is considered.
To determine the particle trajectories, Zhukovskii’s geometric approach [1] is elaborated. It is shown that the trajectory equations obtained by this method are equivalent to the trajectory equations which can be derived from the Lagrange equations by the isoenergetic reduction (Whittaker’s method [2]). The geometric approach enables one to prove that if the external forces are tangent to the particle trajectory (e.g., "dry friction" forces), then the trajectories coincide with the geodesics. This research extends the results obtained in [3]. |
| References |
| 1. | N. E. Zhukovskii, Complete Papers, Vol. 1: General Mechanics
(Glav. Red. Aviats. Lit-ry, Moscow, 1937)
[in Russian]. |
| 2. | E. T. Whittaker, Analytical Dynamics
(Udmurdskii Universitet, Izhevsk, 1999)
[in Russian]. |
| 3. | A. P. Blinov, "On a Particular Case of Motion of a Mass Point,"
Prikl. Mat. Mekh.
63 (5), 781-784 (1999)
[J. Appl. Math. Mech. (Engl. Transl.)]. |
| 4. | A. P. Norden, A Short Course in Differential Geometry
(Fizmatgiz, Moscow, 1958)
[in Russian]. |
| 5. | P. Appel, Theoretical Mechanics. Vol. 1
(Fizmatgiz, Moscow, 1960)
[in Russian]. |
| 6. | G. Lamb, Theoretical Mechanics. Vol. 2
(Glav. Red. Obshchetekhn. Lit-ry, Moscow, 1935)
[in Russian]. |
| 7. | F. G. Tricomi, Differential Equations
(Izd-vo Inostr. Lit-ry, Moscow, 1962)
[in Russian]. |
|
| Received |
08 January 2004 |
| Link to Fulltext |
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