Umahinieseproject2

Umahinieseproject2 - Iniese Bernard Umah MA 280 Mathlab...

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Unformatted text preview: Iniese Bernard Umah MA 280 Mathlab Assignment #2 Prof Decir A) syms t ezplot3(t*cos(t), t*sin(t), t, [-4 4]) x = t c os (t ), y = t s in (t ), z = t 4 2 z 0 -2 -4 2 4 0 2 0 -2 -2 y -4 -4 x B) syms t real; r = [t*cos(t), t*sin(t), t]; /* rp = velocity */ rp = diff(r) rp = [ cos(t) - t*sin(t), sin(t) + t*cos(t), 1] % rs = speed % rs = sqrt(dot(rp, rp)) rs = (t^2 + 2)^(1/2) /* ra = acceleration */ ra = diff(rp) ra = Iniese Bernard Umah MA 280 Mathlab Assignment #2 Prof Decir [ - 2*sin(t) - t*cos(t), 2*cos(t) - t*sin(t), 0] C) T = rp/rs T= [ (cos(t) - t*sin(t))/(t^2 + 2)^(1/2), (sin(t) + t*cos(t))/(t^2 + 2)^(1/2), 1/(t^2 + 2)^(1/2)] DT = diff(T) DT = [ - (2*sin(t) + t*cos(t))/(t^2 + 2)^(1/2) - (t*(cos(t) - t*sin(t)))/ (t^2 + 2)^(3/2), (2*cos(t) - t*sin(t))/(t^2 + 2)^(1/2) - (t*(sin(t) + t*cos(t)))/(t^2 + 2)^(3/2), -t/(t^2 + 2)^(3/2)] K= sqrt(dot(DT,DT))/rs K= (t^4 + 5*t^2 + 8)^(1/2)/(t^2 + 2)^(3/2) D) ezplot(K) (t 4 + 5 t 2 + 8 )1 /2 /(t 2 + 2 )3 /2 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 -6 E) -4 -2 0 t 2 4 6 Iniese Bernard Umah MA 280 Mathlab Assignment #2 Prof Decir UT = rp/rs UT = [ (cos(t) - t*sin(t))/(t^2 + 2)^(1/2), (sin(t) + t*cos(t))/(t^2 + 2)^(1/2), 1/(t^2 + 2)^(1/2)] DUT = diff(UT) /*unit tangent vector*/ DUT = [ - (2*sin(t) + t*cos(t))/(t^2 + 2)^(1/2) - (t*(cos(t) - t*sin(t)))/ (t^2 + 2)^(3/2), (2*cos(t) - t*sin(t))/(t^2 + 2)^(1/2) - (t*(sin(t) + t*cos(t)))/(t^2 + 2)^(3/2), -t/(t^2 + 2)^(3/2)] UN = (DUT)/sqrt(dot(DUT, DUT)) /*unit normal vector*/ UN = [ -((t^2 + 2)*((2*sin(t) + t*cos(t))/(t^2 + 2)^(1/2) + (t*(cos(t) t*sin(t)))/(t^2 + 2)^(3/2)))/(t^4 + 5*t^2 + 8)^(1/2), ((t^2 + 2)*((2*cos(t) - t*sin(t))/(t^2 + 2)^(1/2) - (t*(sin(t) + t*cos(t)))/ (t^2 + 2)^(3/2)))/(t^4 + 5*t^2 + 8)^(1/2), -t/((t^2 + 2)^(1/2)*(t^4 + 5*t^2 + 8)^(1/2))] F) aT =diff( rs) /* tangential component of acceleration*/ aT = t/(t^2 + 2)^(1/2) /* Normal component acceleration*/ aN = sqrt((sqrt(dot(ra, ra)))^2-(aT)^2) aN = (t^2 - t^2/(t^2 + 2) + 4)^(1/2) simplify(aN) ans = (t^4 + 5*t^2 + 8)^(1/2)/(t^2 + 2)^(1/2) ...
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Umahinieseproject2 - Iniese Bernard Umah MA 280 Mathlab...

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