An astroid is the four-cusped plane curve parametrized by , for . It appears as the relative trajectory in the astroid motion of a harmonic oscillator in a rotating frame. The parametrization has zero first derivative at the cusps while remaining smooth as a function of its parameter.
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An "astroid" refers to a particular type of mathematical curve, specifically a hypocycloid with four cusps. It is defined as the path traced by a point on the circumference of a smaller circle that rolls within a larger circle, where the radius of the smaller circle is one-fourth that of the larger one.