Geodesic
Mathematical model of the snakeboard
Matematičeskoe modelirovanie, Tome 18 (2006) no. 5, pp. 37-48.

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper investigates a simplified mathematical model of a derivative of a skateboard known as the Snakeboard. Equations of motion of the model are represented in Appell's form. Analytical and numerical investigation of these equations is performed. The basic snakeboard gaits (forward gait, rotate gait, transverse gait) are analyzed. 
@article{MM_2006_18_5_a4,
     author = {A. S. Kuleshov},
     title = {Mathematical model of the snakeboard},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {37--48},
     publisher = {mathdoc},
     volume = {18},
     number = {5},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2006_18_5_a4/}
}
TY  - JOUR
AU  - A. S. Kuleshov
TI  - Mathematical model of the snakeboard
JO  - Matematičeskoe modelirovanie
PY  - 2006
SP  - 37
EP  - 48
VL  - 18
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2006_18_5_a4/
LA  - ru
ID  - MM_2006_18_5_a4
ER  - 
%0 Journal Article
%A A. S. Kuleshov
%T Mathematical model of the snakeboard
%J Matematičeskoe modelirovanie
%D 2006
%P 37-48
%V 18
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2006_18_5_a4/
%G ru
%F MM_2006_18_5_a4
A. S. Kuleshov. Mathematical model of the snakeboard. Matematičeskoe modelirovanie, Tome 18 (2006) no. 5, pp. 37-48. http://geodesic.mathdoc.fr/item/MM_2006_18_5_a4/

[1] A. D. Lewis, J. P. Ostrowski, R. M. Murray, J. W. Burdick, “Nonholonomic mechanics and locomotion: the Snakeboard example”, Proceedings of the IEEE ICRA (San Diego, May 1994, IEEE), 2391–2400

[2] J. P. Ostrowski, J. W. Burdick, A. D. Lewis, R. M. Murray, “The Mechanics of Undulatory Locomotion: The Mixed Kinematic and Dynamic Case”, Proceedings of the IEEE ICRA (Nagoya, Japan, May 1995, IEEE), 1945–1951

[3] J. P. Ostrowski, The Mechanics and Control of Undulatory Robotic Locomotion, Ph.D. thesis, California Institute of Technology, Pasadena, California, USA, Sept. 1995

[4] A. M. Bloch, P. S. Krishnaprasad, J. E. Marsden, R. M. Murray, “Nonholonomic Mechanical Systems with Symmetry”, Archive for Rational Mechanics and Analysis, 136:1, 21–99 | DOI | MR | Zbl

[5] W. S. Koon Marsden, “Optimal control for holonomic and nonholonomic mechanical systems with symmetry and Lagrangian reduction”, SIAM J. Control Optim., 35:3 (1997), 901–929 | DOI | MR | Zbl

[6] J. P. Ostrowski, J. P. Desai, V. Kumar, “Optimal gait selection for nonholonomic locomotion systems”, Internat. Journ. Robotics Res., 19:5 (2000), 225–237 | DOI

[7] F. Bullo, A. D. Lewis, “Kinematic controllability and motion planning for the snakeboard”, IEEE Transactions on Robotics and Automation, 19:3 (2003), 494–498 | DOI

[8] Yu. I. Neimark, N. A. Fufaev, Dinamika negolonomnykh sistem, Nauka, M., 1967, 519 pp.

[9] A. I. Lure, Analiticheskaya mekhanika, Gos. izd-vo fiz.-mat. lit-ry, M., 1961, 824 pp. | MR

[10] Yu. G. Ispolov, B. A. Smolnikov, “Skateboard Dynamics”, Computer Methods in Applied Mechanics and Engineering, 131 (1996), 327–333 | DOI | Zbl

[11] V. F. Zaitsev, A. D. Polyanin, Spravochnik po obyknovennym differentsialnym uravneniyam, Nauka, Fizmatlit, M., 1995, 559 pp. | MR