CoriolisAcceleration::usage=" References: Hollis, Selwyn. CalcLabs with Mathematica, Multivariable Calculus. Belmont, CA: Cengage Learning, p. 175, 2010.; Personal";
​
Consideraunitarysphere,centeredontheorigin,rotatingaroundtheZaxis,inthewest-eastdirection,withaconstantangularvelocity​​ω=2π.Assumethatthereisaninsectthattravelsnorthonthespherewithanangularvelocity​​η=
π
2
andit'slocatedatthepoint{1,0,0},ontheequatoratt=0.Thepositionoftheinsectisgivenby​​γ[t]={Cos[ηt]Cos[ωt],Cos[ηt]Sin[ωt],Sin[ηt]}para0≤t≤1.
In[]:=
​​​​​​Animate​​γ[t_]:=Cos
π
2
tCos[πt],Cos
π
2
tSin[πt],Sin
π
2
t;​​a0[t_]:=-
2
π
+
2
π
4
Cos
π
2
t{Cos[πt],Sin[πt],0};​​ac[t_]:=-
2
π
Sin
π
2
t{-Sin[πt],Cos[πt],0};​​ak[t_]:=0,0,-
2
π
4
Sin
π
2
t;​​a[t_]:=a0[t]+ac[t]+ak[t];​​ξ[t_]:={Cos[2πt],Sin[2πt],0};​​​​Show[ParametricPlot3D[γ[t],{t,0,t1},PlotStyleDirective[Dashed,Thick,Black]],Graphics3D[{Black,Ball[γ[t],0.02]/.tt1-0.01}],​​ParametricPlot3D[ξ[t],{t,0,1}],​​SphericalPlot3D[1,{ϕ,0,π},{θ,0,2πt1},Mesh{12,24},MeshStyle->Gray,PlotStyleNone],Graphics3D[{Black,Point[γ[t]],Arrowheads[.05],Arrow[Tube[{γ[t],γ[t]+0.1a[t]}]]}]/.tt1-0.01,​​​​Graphics3D[{Green,Point[γ[t]],Arrowheads[.05],Arrow[Tube[{γ[t],γ[t]+0.1a0[t]}]]}]/.tt1-0.01,​​​​Graphics3D[{Yellow,Point[γ[t]],Arrowheads[.05],Arrow[Tube[{γ[t],γ[t]+0.5ak[t]}]]}]/.tt1-0.01,​​Graphics3D[{Purple,Point[{0,0,0}],Arrowheads[.01],Arrow[Tube[{{0,0,0},{0,0,0}+ξ[t]},0.01]]}]/.tt1-0.01,​​​​Graphics3D[{Red,Point[γ[t]],Arrowheads[.05],Arrow[Tube[{γ[t],γ[t]+0.2ac[t]}]]}]/.tt1-0.01,AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},ViewPoint{1,1,1},AxesTrue,BoxedFalse,PlotRangeAll,PerformanceGoal"Quality",ImageSize900],{t1,0.00001,1,0.00001},AnimationRunningFalse
Out[]=
t1
The acceleration of Coriolis appears in red, deflecting the trajectory of the insect.
What other components of acceleration apart from that of Coriolis, appear in the graph?