I am trying to find the normal and tangent of acceleration. I know the formula for the tangent of acceleration is $((Acceleration . Velocity)/(Velocity.Velocity))*Velocity$ and the normal of acceleration is the same but with $Velocity$ replaced with the perpendicular of velocity. I think my errors arise because I am trying to manipulate parametric functions incorrectly.
Anyway, here is my attempt:
Clear[t,x,y,z,P,velocity,acceleration,atan,tanvector];
x[t_] = 2 Sin[t];
y[t_] = 6 Sin[t/2]^2;
z[t_] = 3 Cos[t];
P[t_] = {x[t], y[t], z[t]};
curveplot = ParametricPlot3D[P[t],{t,1,6},PlotStyle->Thickness[0.01]];
velocity[t_] = {x'[t], y'[t], Z'[t]};
acceleration[t_] = {x''[t], y''[t], z''[t]};
atan[t_] = ((acceleration[t].velocity[t])/(velocity[t].velocity[t]))*velocity[t];
tanvector[t_]:= Vector[atan[t],Tail->P[t],VectorColor->Blue]
Show[curveplot,Table[tanvector[t],{t,1,6,(6-1)/10}],
PlotRange -> All, AxesLabel -> {"x","y","z"}]
This question is different from this question: Finding unit tangent normal and binormal vectors because I am asking for the tangent and normal of acceleration using the equation: $((Acceleration . Velocity)/(Velocity.Velocity))*Velocity$.
I am missing an undertanding of how to manipulate parametric plots.
Dot
product, you should use a period, not a center dot:acceleration[t].velocity[t]
, and so forth. $\endgroup$