Geodesic
Examples of topological approach to the problem of inverted pendulum with moving pivot point
Russian journal of nonlinear dynamics, Tome 10 (2014) no. 4, pp. 465-472.

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

Two examples concerning application of topology in study of dynamics of inverted plain mathematical pendulum with pivot point moving along horizontal straight line are considered. The first example is an application of the Ważewski principle to the problem of existence of solution without falling. The second example is a proof of existence of periodic solution in the same system when law of motion is periodic as well. Moreover, in the second case it is also shown that along obtained periodic solution pendulum never becomes horizontal (falls).
Keywords: inverted pendulum, Ważewski principle, periodic solution.
Mots-clés : Lefschetz–Hopf theorem 
@article{ND_2014_10_4_a5,
     author = {Ivan Yu. Polekhin},
     title = {Examples of topological approach to the problem of inverted pendulum with moving pivot point},
     journal = {Russian journal of nonlinear dynamics},
     pages = {465--472},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2014_10_4_a5/}
}
TY  - JOUR
AU  - Ivan Yu. Polekhin
TI  - Examples of topological approach to the problem of inverted pendulum with moving pivot point
JO  - Russian journal of nonlinear dynamics
PY  - 2014
SP  - 465
EP  - 472
VL  - 10
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2014_10_4_a5/
LA  - ru
ID  - ND_2014_10_4_a5
ER  - 
%0 Journal Article
%A Ivan Yu. Polekhin
%T Examples of topological approach to the problem of inverted pendulum with moving pivot point
%J Russian journal of nonlinear dynamics
%D 2014
%P 465-472
%V 10
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2014_10_4_a5/
%G ru
%F ND_2014_10_4_a5
Ivan Yu. Polekhin. Examples of topological approach to the problem of inverted pendulum with moving pivot point. Russian journal of nonlinear dynamics, Tome 10 (2014) no. 4, pp. 465-472. http://geodesic.mathdoc.fr/item/ND_2014_10_4_a5/

[1] Courant R., Robbins H., What is mathematics?: An elementary approach to ideas and methods, 2nd ed., Oxford Univ. Press, New York, 1996, 592 pp. | MR | Zbl

[2] Arnold V. I., Chto takoe matematika?, MTsNMO, M., 2002, 104 pp.

[3] Srzednicki R., Wójcik K., Zgliczyński P., “Fixed point results based on the Ważewski method”, Handbook of topological fixed point theory, eds. R. Brown, M. Furi, L. Górniewicz, B. Jiang, Springer, Dordrecht, 2005, 905–943 | DOI | MR

[4] Ważewski T., “Sur un principe topologique de l'examen de l'allure asymptotique des intégrales des équations différentielles ordinaires”, Ann. Soc. Polon. Math., 20 (1947), 279–313 | MR

[5] Hartman Ph., Ordinary differential equations, Classics Appl. Math., 38, Wiley, New York, 1964, 612 pp. | MR

[6] Reissig R., Sansone G., Conti R., Qualitative Theorie nichtlinearer Differentialgleichungen, Edizioni Cremonese, Rome, 1963, 381 pp. | MR | Zbl