English: Plot of a trajectory of a badminton shuttlecock. The trajectory follows the differential equation ${\displaystyle {\ddot {\vec {r}}}(t)=-k\,v\cdot {\vec {v}}-g\cdot {\hat {\vec {y}}}}$ with initial conditions ${\displaystyle {\vec {r}}(0)=(0,2.5\,\mathrm {m} )}$, ${\displaystyle {\dot {\vec {r}}}(0)=v_{0}({\hat {\vec {x}}}\cos(\alpha _{0})+{\hat {\vec {y}}}\sin(\alpha _{0}))}$.

The parameters are:

• ${\displaystyle g=9.81\,\mathrm {m/s^{2}} }$, ${\displaystyle k=0.2\,\mathrm {m^{-1}} }$, ${\displaystyle v_{0}=65\,\mathrm {m/s} }$
• Trajectories are drawn for different launching angles ${\displaystyle \alpha _{0}=20^{\circ }}$, ${\displaystyle \alpha _{0}=30^{\circ }}$, ${\displaystyle \alpha _{0}=40^{\circ }}$, ${\displaystyle \alpha _{0}=50^{\circ }}$, ${\displaystyle \alpha _{0}=60^{\circ }}$

The differential equation is solved numerically using Scipy odeint.