Chapter 7, Problem 27P

In MATLAB write out a program to integrate the equations of motion of a rigid body. The inertia matrix is given by I = [125 0 0; 0 100 0; 0 0 75] which is a diagonal, where diag operator provides a matrix with given elements placed on its diagonal. Consider three cases where the body rotates 1 rad/sec about each principal axis. Integrate the resulting motion and study the angular rates and the resulting attitude (use any attitude coordinates). For each principal axis case, assume first that a pure spin about the principal axis is performed, and then repeat the simulation where a small 0.1 rad/sec motion is present about another principal axis. Discuss the stability of each motion. The code should produce a total of 6 simulations results when it is ran.

Q. A strain gauge rosette that is attached to the surface of a stressed component C). If the strain gauge rosette is of the D° gives 3 readings (a = A, b = B, &c = type (indicating the angle between each of the gauges), construct a Mohr's Strain Circle overleaf. You should assume that gauge A is aligned along the x-axis. Using the Mohr's Strain Circle calculate the: [10 marks] 100 918 ucy evods gringiz ya mwo quoy al etsede 39 926919 (i) principal strains (1, 2)? (au) oniona [5 marks] (ii) principal angles (1, 2)? You should measure these anticlockwise from the y-axis. 20 [5 marks] (iii) maximum shear strain in the plane (ymax)? Ex = Ea Ey = εc [5 marks] (epol) (apob) é Ea = A = -210 2 B=E₁ = -50 E₁ = C = 340 D = 45° bril elled ✓A bedivordan nemigas olloho shot on no eonsoup Imeneo alubom shine sail-no viss ieqse sidetiva bnat sabied 2

1) Solve and show which is converage or diyverage a = 2+(0.1)" 3 16) a = n 1-2n 2) a = In n 1+2n 17) a = n 1-5n4 3) an = n* +8n³ 18) a =√4"n n² -2n+1 n! 20) a = 4) a₁ = 10 n-1 (Ina) 5) a=1+(-1)" 21) a= 6) a 7) an = * = (12+) (1-1) 2n (-1)+1 2n-1 3n+1 22) a= 3n-1 x" 23) a= .x>0 2n+1 2n 3"x6" 8) a = 24) a = n+1 π 9) a = sin 2 sin n 10) an = n + 2 x n! 25) a = tanh(n) n² 1 26) a = -sin- 2n-1 27) a = tan(n) n n 11) a = 2" 12) a = n 13) a = 8/ +=(1+2)" 14) a = 15) a = √10n In(n+1) 29) a = n 30) an-√n²-1 1 28) a = + √2" (In n)200 n 31) a=- = 1 dx nix