Question

F=100N, md=100lb, L=60ft, mr=2000lb

Problems. The sky crane was a novel solution to the problem of landing the 2000 lb Curiosity rover on the surface of Mars. Curiosity hangs from the descent stage by 60-foot-long nylon tethers (Figure 2). The descent stage uses its thrusters to hover as the rover is lowered to the surface. Thus the rover behaves like a pendulum whose base is moving. A model of it is shown in Figure 2b. The rover mass is me, the descent stage muss is md, and the net horizontal component of the thruster forces is £. Among other simplifications, this model does not take into account vertical motion and any rotational motion of the descent vehicle. 1. Draw a detailed FBD 2. Do not substitute the parameter values yet (keep using symbolic variables m m. Land / ), and derive the EOM using the Lagrangian approach in terms of the angle and the displacement x, with the force fas the given input. Do not substitute the parameter values yet (keep using symbolic variables m.m.Land / and express the EOM as a set of first order ODES. Do not substitute the parameter values yet (keep using symbolic variables m m . L and/), and obtain the transfer function of the system G(S)= () F(s) Substitute the parameter values in your result of problem (3) Substitute the parameter values in your result of problem (4).

Answer 1

F62 l(1-es Raso: 2) hare v2 l 2012 + 2l Bricoso Kineti Energy (ke) - Makit įmova Myat sumy (228'44'42118650) Poftutial luogy et) -mole (1-6050) -F by lagrange Equation 0 fone Mod + mom' + mo l8 Coxo -m. losino = F foro mp4 3* + my li cosol moglsino = 0 — for small angles sine : o, coso - 1 and loti + mgo=0 Trake leaplace of ① (1s²-g) ols) = 8² x (6) (289) take leaplace of → (Ml + My ) 5² x (s) + mo lst ( 82 (s) = f (8)

t POST ree 5+2 5+3)}- [lu mostrara)-mex] 7© $2 let x = 9, = $a => keying in 6 and 4 and lag ranging (Md + Mr J, + my life = f . s) and = 32 94 9 lemping values info y = -57,14 % +0.048 and & - - - - - 0.163581) keeping value in 6 6 X(6) 605² + 9.81 FO) $210052 [605249-81) - 12000054