Y
Ingenieurmathematik Prüfung 2
9.Dez.2010
Zeit 90 Minuten, Reihenfolge beliebig, 8 Punkte pro Hauptaufgabe,
40 Pt. = N.6.
en
und dkrit
an für die Hesse'sche Normalform der zur y-z-Ebene
parallelen Ebene x = 4
.
en = [1 0 0], dkrit = 4
z = exp(-i*10*pi/2) = exp(-i*5*pi) = exp(-i*pi) = -1
u = [q ; q ; -2]
,
und v = [-1 ; 2 ; 4]
zueinander orthogonal sind.
-1*q + 2*q -8 = 0 ; q = 8
A = [-5 -5 0]' B = [5 -5 0]' S = [0 0 7]' SA = A - S SB = B - S w = acosd(SA'*SB/(norm(SA)*norm(SB))) %SA = -5 -5 -7 %SB = 5 -5 -7 %w = 60.3336
xc = 0, yc = 3, r = 3 w0 = 0 gh = 8/2 n = 2 t = 0:pi/200:n*2*pi; x = r*cos(t+w0) + xc; y = r*sin(t+w0) + yc; z = gh*t/(2*pi); plot3(x,y,z) hold on axis equal PSE = [3 3 3; 3 3 3; 0 4 8] plot3(PSE(1,:),PSE(2,:), PSE(3,:),'ko') PM = [-3 -3 ; 3 3 ; 2 6] plot3(PM(1,:),PM(2,:), PM(3,:),'ko') P1 = [0 0 3]' plot3(P1(1),P1(2), P1(3),'ro') P2 = [0 0 7]' plot3(P2(1),P2(2), P2(3),'ro') plot3([0 0],[0 0],[ 0 8],'r') box on view(15,64) hold off
A = [0 0 0]' , B = [3 0 0]' C = [3 -4 0]' , D = [0 -4 0]' E = [0 0 3.2]' , F = [3 0 3.2]' G = [3 -4 3.2]' , H = [0 -4 3.2]' u = G - B v = D - B N = cross(u,v) lN = norm(N) en1 = N/lN dkrit1 = en1'*B % Distanztests A H F dA = en1'*A-dkrit1 dF = en1'*F-dkrit1 dH = en1'*H-dkrit1 %u = 0 -4 3.2 %v = -3 -4 0 %N = 12.8000 -9.6 -12.0000 %lN = 20 %en1 = 0.6400 -0.48 -0.6000 %dkrit1 = 1.9200 %dA = -1.9200 %dF = -1.9200 %dH = -1.9200 en2 = en1 dkrit2 = en2'*A % = 0
Koi = [4 8 8 4 4; 0 0 6 6 0; 1 1 1 1 1] Tray = [1 0 0; 0 1 -3 ; 0 0 1] My = [1 0 0; 0 -1 0; 0 0 1] Trby = [1 0 0; 0 1 3 ; 0 0 1] Trax = [1 0 -6; 0 1 0 ; 0 0 1] Mx = [-1 0 0; 0 1 0; 0 0 1] Trbx = [1 0 6; 0 1 0 ; 0 0 1] Ttot = Trbx * Mx * Trax * Trby * My * Tray Kof = Ttot*Koi