Geodesic
Moto di una bicicletta con ruote non circolari
Matematica, cultura e società, Série 1, Tome 4 (2019) no. 2, pp. 145-157.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Su quale terreno può rotolare senza scivolare una ruota non circolare? Sulla questione, di cui si sono interessate le cronache perché è stata proposta come tema agli esami della Scuola Media Superiore del 2017, richiamiamo alcune proposte presenti in letteratura e formuliamo qualche ulteriore osservazione.
What kind of ground may allow a noncircular wheel to roll without sliding? Such a question has been proposed in final national exams of the Italian high school system in 2017, and it attracted attention in the news. Here, we review some available pertinent answers, adding further remarks. 
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Frosali, Giovanni; Mariano, Paolo Maria. Moto di una bicicletta con ruote non circolari. Matematica, cultura e società, Série 1, Tome 4 (2019) no. 2, pp. 145-157. http://geodesic.mathdoc.fr/item/RUMI_2019_1_4_2_a9/

[1] Ali S. (2017), A unified dynamic algorithm for wheeled multibody systems with passive joints and nonholonomic constraints, Multibody Syst. Dyn., 41, 317-346. | DOI | MR | Zbl

[2] Boyer F., Porez M., Mauny J. (2018), Reduced dynamics of the non-holonomic Whipple bicycle, J. Nonlinear Sci., 28, 483-493. | DOI | MR | Zbl

[3] Chen C.-K., Chu T.-D., ZHANG, X.-D. (2019), Modeling and control of an active stabilizing assistant system for a bicycle, Sensors, 19, art. n. 248.

[4] Escalona J. L., Recuero A. M. (2012), A bicycle model for education in multibody dynamics and real-time interactive simulation, Multibody Syst. Dyn., 27, 383-402. | DOI | MR | Zbl

[5] Getz N. H., Marsden J. E. (1995), Control for an autonomous bicycle, Proc. 1995 IEEE Int. Conf. Robotics Autom., 2, 1397-1402.

[6] Górecki H. (2018), Mathematical model of a bicycle and its stability analysis, Studies in Systems, Decision and Control, 107, 641-663.

[7] Hall L., Wagon S. (1992), Roads and wheels, Math. Mag., 65, 283-301. | DOI | MR | Zbl

[8] Herlihy D. V. (2004) Bicycle: The history. New Haven and London:Yale University Press.

[9] Koon W. S., Marsden J. E. (1997), The Hamiltonian and Lagrangian approaches to the dynamics of nonholonomic systems, Rep. Math. Phys. , 40, 21-62. | DOI | MR | Zbl

[10] Jeong H. B., Ahn C. K., You S. H., SOHN, K. M. (2019), Finite-memory estimation for vehicle roll and road bank angles, IEEE Trans. Ind. Elect. , 66, 5423-5432.

[11] Levi M. (2017), Schrödinger's equation and “bike tracks”, J. Geom. Phys., 115, 124-130. | DOI | MR | Zbl

[12] Limebeer D. J. N., Sharma A. (2010), Burst oscillations in the accelerating bicycle, J. Appl. Mech. Trans. ASME, 77, art. n. 061012.

[13] Macdermid P. W., Fink P. W., Miller M. C., Stannard S. (2017), The impact of uphill cycling and bicycle suspension on downhill performance during cross-country mountain biking, J. Sports Sci. , 35, 1355-1363.

[14] Merten E. A. (2014), Application of evolutionary structural optimisation; reinventing the (bicycle) wheel, Appl. Mech. Mat. , 553, 830-835.

[15] Meijaard J. P., Papadopoulos Jim M., Ruina A., Schwab A. L. (2011), History of thoughts about bicycle self-stability. http://arxiv.org, 2011. eCommons@Cornell. | Zbl

[16] MoMath National Museum of Mathematics, http://momath.org/

[17] Robison I. G. B. (1960), Rockers and rollers, Math. Mag., 33, 139-144. | Zbl

[18] Rozenblat G. M. (2016), The controlled motion of a bicycle, J. Appl. Math. Mech., 80, 133-140. | DOI | MR | Zbl

[19] Schwab A. L., De Lange P. D. L., Happee R., Moore J. K. (2013), Rider control identification in bicycling using lateral force perturbation tests, Proc. Inst. Mech. Eng.s, Part K: J. Multi-body Dyn., 227, 390-406.

[20] Spicer J. B. (2013), Effects of the nonlinear elastic behavior of bicycle chain on transmission efficiency, J. Appl. Mech. Trans. ASME, 80, art. n. 021005.

[21] Tabachnikov S. (2017), On the bicycle transformation and the filament equation results and conjectures, J. Geom. Phys., 115, 116-123. | DOI | MR | Zbl

[22] Wilson D. G. (2004). Bicycling Science. The MIT Press, 3rd edition.

[23] Wu Y.-C., Chen L.-A. (2016), A gear-shifting mechanism with a rotary configuration for applications in a 16-speed bicycle transmission hub, Trans. Canadian Soc. Mech. Eng., 40, 597-606.

[24] Zagorski S. B. (2019), Derivation of a multi-body model of an articulated vehicle, Int. J. Vehicle Perf., 5, 129-164.