By Fowles G.R., Cassiday G.L.
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The change of the generalized coordinates y, ϕ is shown in Fig. I. 4, and that of the coordinates x, ϕ1 is shown in Fig. I. 5. We see that at the stage of the driving wheels slipping, the coordinate ϕ1 rapidly increases. Note that, if tyres are compliant and the traction coeﬃcient depends continuously on the speed, the curves in ﬁgures I. 2 and I. 3 will be replaced with continuous ones. However, a sharp change of the driving force and acceleration at the instants t1 and t2 remains. C h a p t e r II NONHOLONOMIC SYSTEMS From the analog of Newton’s law, Maggi’s equations are deduced which are the most convenient equations of the nonholonomic mechanics.
2) 1 (c1 (y + L1 ϕ)2 + c2 (y − L2 ϕ)2 ) . 2 Here Lk (k = 1, 2) are the horizontal distances from the point C to the points Bk (see Fig. I. 1). 3) 1 = (χx˙ 2 + χ1 (y˙ + L1 ϕ) ˙ 2 + χ2 (y˙ − L2 ϕ) ˙ 2) . 2 Let us take into consideration the drive moment Θdr and the moment of rolling friction of the wheels. The elementary work of generalized forces applied to the driving front wheels is the product of the drive moment Θdr by the angular displacement δϕ1 and the moment of rolling friction by the angular displacement δϕ1 .
Veselov, L. E. Veselova, V. Ya. Gershkovich, C. Godbillon, V. V. Kozlov, M. Le´on, L. M. Markhashov, A. I. Neishtadt, N. N. Petrov, P. Rodrigues, D. M. Sintsov, S. Smale, L. D. Faddeev, D. P. Chevallier and others [6, 7, 33, 35, 38, 48, 63, 149, 181, 209, 293, 344, 349, 354, 386, 397, 413]. Particular signiﬁcance for their understanding has the treatises of V. I. Arnol’d , A. D. Bruno , and B. A. Dubrovin, S. P. Novikov, A. T. Fomenko , C. Truesdell . Note that the present survey and references do not contain unfortunately many highly important works.
Analytical mechanics by Fowles G.R., Cassiday G.L.