Manual solution fo Advanced, Study notes of Mechanics

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CHAPTER G &t Given ¥ [5 constant. a 7 EKO Find velouty eonstrammt ¢ delermme ge ae 1€ af ts holonome, % Solution: Define 9, = 75,947 ¥, 99°2 Ty Heit Yo ZU leoslres di rsialr+9)7} Uy ta Xe Vg cosl7+9), Uy-F ~Jg= vy sinlvee) Eliminate vg, which 15 nota generalized coordina fe: Hp sire ®)- Jy cosly +e) = 0 Standard Foran ray >sintres), 4a = es (748),4,3=0, b, =O F holotomic xf = 9, salr+8) f = preost ree), 2h so Last equation reguices that € 1s de pendent of @ which contradicts first two ezuetion => Constraint 1s nonholonomic, Given Constant translahorel u. Find veloaty constramnt 04 X,Y coordinates of siiderS ther ax Find Conkigure tion epasteant by mbezration Egeometcrcally, Solution; Fix xy> fo te guide bar, Wsd—>v, Ute raya where Uy = KTP, sue ey, PREY Pe AT paBns TZ Dy T= Re urk (eg,0, UT =Ve2and (ey,2) qd integrate C1): dks udlrdn we Xauten tex “ tnkegrafe (2); AV = aprdee Yssrtecy Bub Xeul ¢ YO when x=02¢,2C,¢0 Xsubt aM sr Tg+ (coset 5/4 Oj = 0 G2eose X-c0s9 4 (7 tOL 5:08 )(-sene 20% jst Ll-0 or ¥sine+ BR BP 20 d To obtain eorfigu ration constraint, separate vecinbles: dy + (8 $22) d0=0 = dy RA(sig) > y-Bopte Set yO whee Go t/a C=-RS y—-Rigm_-=0 SJ Geometrically: Right triangle ABO R=(yth)508