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Solution: In this case, the system can be modeled as a function with two output signals,
where
where(x(t), y(t)) is the position of the tail in they plane. This model Is Clearly not linear. If the Input torque doubles, for example, the output values will not double. In fact, the output values are constrained to lie on a circle centered at the origin, regardless of the Input. For this reason, the model is BIBO stable. The output is always bounded. Thus, while our previous model was linear and unstable, this one Is nonlinear and stable. Which model is more useful?