Solved: CAS PROJECT. Paths of Motions. Gear transmissions
Chapter 9, Problem 9.1.181(choose chapter or problem)
CAS PROJECT. Paths of Motions. Gear transmissions and other engineering constructions often involve complicated paths whose study is greatly facilitated by the use of a CAS. To grasp the idea, graph the following paths and find the velocity, the speed, and the tangential and normal accelerations.
(a) \(\mathbf{r}(t)=[2 \cos t+\cos 2 t, 2 \sin t-\sin 2 t]\)
(b) \(\mathbf{r}(t)=[\cos t+\cos 2 t, \quad \sin t-\sin 2 t]\)
(c) \(\mathbf{r}(t)=\left[\begin{array}{lll}\cos t, & \sin 2 t, & \cos 2 t\end{array}\right]\)
(d) \(\mathbf{r}(t)=[c t \cos t, \quad c t \sin t, \quad c t] \quad(c \neq 0)\)
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