assignment 1

# assignment 1 - dsdt:=(1(4(cos(3 t sin(t)2(—3 sin(3 t...

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Unformatted text preview: dsdt := (1) (4 (cos(3 t) +sin(t))2 (—3 sin(3 t) +cos(t))2 +9 (cos(3 t) —cos(t))4( 1/2 [> dsdt == N07m(diff(Q(t)a t) ); —3 sin(3 t) +sin(t) )2 + (3 005(3 t) +3 cos(t) )2) > Length := evalf(1nt(dsdt, t=0 ..2-Pi ' \/ Length := 45.97703316 (2) > evalf(subs(t=2, Curvature( ( (cos(3 * t) + sin(t) )A2, (cos(3 * t) -cos(t) )A3, sin(3 * t) + 3 I: * Shim) ) )) m (3) l> plot(Curvature(Q(t), t), t=0 ..2'Pi); V evalf(subs(t—. Q(t) ) ); . . 2027 1526)ex + (-3.642323710)ey +‘ s(2.704185087)ez ~ TM) Ivy/1b Wm“ (4) (t) ) ); Wm WM WWW/Q 1095528)ex + (3.588243743 )ey + ( -2.667676736)ez (5) > The maximas occu at approximately t = .97 and t = 4.14 R352 ( . 2 V evalf(subs(t=4.14, .02 MCPI == plot3a’( [0.02202741526, -3.642323710, 2.704185087], x =-1 ..1,y =-1 ..1, style = point, symbol = box, color = blue) : > > MCP2 == plot3d( [0.02211095528, 3.588243743, ~2.667676736], x =-1 ..1,y =-l ..1, style = point, symbol = box, color = blue) : > CURVE == spacecurve( Q(t), t = 0 ..2 -Pi, axes = normal, labels = [x, y, 2], color = black, thickness = 2) : > display( {MCP1, MCP2, CUR VE}) ; T F . E t . [ w [ [ [ l ﬂVllrh/m. I \hlﬂM/‘Pl/I @Yiﬁ Wawm will \ > Spacecurvd Q”), t = 0 __2 - Pi, axes = normal, color = black, thickness = 2, labels = [x, y, 2], orientation = [0, 90]); ...
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assignment 1 - dsdt:=(1(4(cos(3 t sin(t)2(—3 sin(3 t...

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