Velocity & acceleration

> PDEtools[declare](theta(t),r(t), prime=t, quiet):

> T := Rotate('Z',theta(t));

> P := make_POINT(T,r(t),0,0): show(P);

velocity

> VP := project(velocity(P),T): show(VP);

acceleration

> AP := project(acceleration(P),T): show(AP);
#AP := velocity(velocity(P)): show(AP);

Velocity: example 2

> PDEtools[declare](xA(t),yA(t),theta(t),xP(t),yP(t), prime=t, quiet):

> T := Translate(xA(t),yA(t),0) . Rotate('Z',theta(t));

> P := make_POINT(T,xP(t),yP(t),0): show(P);

> VPr := velocity(P,T): show(VPr);

> VPa := velocity(P):
VPa[comps] := map(collect,VPa[comps],[diff(theta(t),t)]):
show(VPa);

Acceleration

> AP := acceleration(P): show(AP);

> APr := acceleration(P,T): show(APr);

> APt := frame_frozen_acceleration(P,T): show(APt);
project(APt,T): show(%);