A Model of Gear Transmission: Fractional Order System Dynamics

Figure 3

First eigen fractional order time components ${\eta }_1(t)$ and ${\zeta }_1(t)$ for different system kinetic and geometric parameter values.

(a) First fractional order mod for different values $\alpha$ ($\alpha =0.25\mathrm{\hspace{0.17em}\hspace{0.17em}}(\text{trace}\mathrm{\hspace{0.17em}\hspace{0.17em}}2)\text{,}$$\alpha =0.5\mathrm{\hspace{0.17em}\hspace{0.17em}}(\text{trace}\mathrm{\hspace{0.17em}\hspace{0.17em}}1)\text{,}$$\alpha =0.75\mathrm{\hspace{0.17em}\hspace{0.17em}}(\text{trace}\mathrm{\hspace{0.17em}\hspace{0.17em}}3)$)

(b) Second mod for different values $\alpha$ ($\alpha =0.25\mathrm{\hspace{0.17em}\hspace{0.17em}}(\text{trace}\mathrm{\hspace{0.17em}\hspace{0.17em}}2)\text{,}$$\alpha =0.5\mathrm{\hspace{0.17em}\hspace{0.17em}}(\text{trace}\mathrm{\hspace{0.17em}\hspace{0.17em}}1)\text{,}$$\alpha =0.75\mathrm{\hspace{0.17em}\hspace{0.17em}}(\text{trace}\mathrm{\hspace{0.17em}\hspace{0.17em}}3)$)

(c) The first coordinate for diferent values  $\alpha$ ($\alpha =0.25\mathrm{\hspace{0.17em}\hspace{0.17em}}(\text{trace}\mathrm{\hspace{0.17em}\hspace{0.17em}}2)\text{,}$$\alpha =0.5\mathrm{\hspace{0.17em}\hspace{0.17em}}(\text{trace}\mathrm{\hspace{0.17em}\hspace{0.17em}}1)\text{,}$$\alpha =0.75\mathrm{\hspace{0.17em}\hspace{0.17em}}(\text{trace}\mathrm{\hspace{0.17em}\hspace{0.17em}}3)$)

(d) The first coordinate for diferent values  $\alpha$ ($\alpha =0\mathrm{\hspace{0.17em}\hspace{0.17em}}(\text{trace}\mathrm{\hspace{0.17em}\hspace{0.17em}}2)$ and $\alpha =0.2\mathrm{\hspace{0.17em}\hspace{0.17em}}(\text{trace}\mathrm{\hspace{0.17em}\hspace{0.17em}}1)$)