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4 A system of two disks. Generalized coordinates are selected as q1 = x , q2 = . The spring constant is equal to c. The smaller disk may roll on a smooth surface. 83) to the two-disk system, we proceed as follows. 85) 1 + MR cos x − MgR(1− cos ) − cx 2. 83) indicate and insert them into it to obtain M+ 3 m x + MR cos 2 − MR sin 3 MR + MR cos x + MgR sin = 0.

W. S. J. Sussmann, Boston, MA: Birkhauser. Carvallo, C. 1902. L’electricite de l’experience et ramenee au principe dex travaux virtuels. Coll. Scienta 19. A. 1897. About a motion of a heavy body on a horizontal plane. In Izbrannye trudy klassiki nauki, 363–375. Moscow: Nauka (in Russian). , and E. Bayo. 1994. Kinematic and dynamic simulation of multibody systems. Mech. Eng. Series. Berlin: Springer-Verlag. , G. Oriolo, L. R. Giordano. 2002. Experiments in visual feedback control of a wheeled mobile robot.

The velocities ω ξ , ω η , ω ζ are quasi-velocities, which may be presented using Euler’s angles , ψ , as follows: ω ξ = ψ sin sin + cos , ω η = ψ sin cos − sin , ω ζ = ψ cos + . 10), we obtain ψ sin − ψ sin + 2ψ 2 cos + ψ 3 sin2 cos − λ(ψ 2 sin + ) 2 3/ 2 = 0. 12) is task based and it is second order nonholonomic. 9: Galiulin and Korenev Example Galiulin and Korienev worked on missiles control and guidance (Galiulin 1971; Korieniev 1964). , tracking a moving target. 10. 9 Motion of a body about a fixed point.

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PIC Microcontrollers: 50 Projects for Beginners & Experts by Bert Van Dam


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