I have a vector $<x(t),y(t),z(t)>$ constrained to a unit sphere. I am trying to plot what the vector looks like as time progresses. What would be the easiest approach to visualizing this?
x[t_, α_] := -1/Sqrt[1 + α^2] Sin[ t Sqrt[1 + α^2]] y[t_, α_] := -α/(1 + α^2) (Cos[t Sqrt[1 + α^2]] - 1) z[t_, α_] := -1 - (1 - Cos[t Sqrt[1 + α^2]])/(1 + α^2)
I want to plot the vector as a function of t [0,10] and I guess alpha=1.