Project-I-sol.html

restart; 1

with(plots); 1

with(linalg); 1

interface(showassumed = 0); 1

1

assume(t::real); 1

lowt := -2; 1

-2

hight := 2; 1

r := [cos(t), sin(t), t]; 1

[cos(t), sin(t), t]

v := diff(r, t); 1

[-sin(t), cos(t), 1]

s := sqrt(innerprod(v, v)); 1

(1+sin(t)^2+cos(t)^2)^(1/2)

s := simplify(s); 1

2^(1/2)

T := v/s; 1

1/2*([-sin(t), cos(t), 1])*2^(1/2)

N := (diff(T, t))/simplify(sqrt(innerprod(diff(T, t), diff(T, t)))); 1

(1/2*([-cos(t), -sin(t), 0])*2^(1/2)+1/8*([0, 0, 0])*2^(1/2))*2^(1/2)

rf := unapply(r, t); 1

proc (t) options operator, arrow; [cos(t), sin(t), t] end proc

Tf := unapply(T, t); 1

proc (t) options operator, arrow; 1/2*([-sin(t), cos(t), 1])*2^(1/2) end proc

Nf := unapply(N, t); 1

proc (t) options operator, arrow; (1/2*([-cos(t), -sin(t), 0])*2^(1/2)+1/8*([0, 0, 0])*2^(1/2))*2^(1/2) end proc

c1 := spacecurve(convert(r, list), t = lowt .. hight, axes = normal, thickness = 3); 1

c1 := spacecurve(convert(r, list), t = lowt .. hight, axes = normal, thickness = 3); 1

Plot

nframes := 20; 1

20

deltat := (hight-lowt)/nframes; 1

1/5

d1 := display(trips, insequence = true); 1

Plot

display(c1, d1, scaling = constrained); 1

Plot