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The diagram depicts a linkage that is situated in the horizontal plane. Collar A slides along the stationary guide bar, and the steerable wheel B at the other end of rigid bar AB rolls over the ground. A servomotor controls the steering angle β. There is no slippage in the rolling motion, so the velocity of end B must be in the sense shown in the diagram. Movement is actuated by the known force F (t) applied to the collar. Generalized coordinates are the horizontal position xA and the rotation angle θ. Use the method of Lagrange multipliers to derive the equations of motion governing these variables.
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