EBK SYSTEM DYNAMICS
EBK SYSTEM DYNAMICS
3rd Edition
ISBN: 9780100254961
Author: Palm
Publisher: YUZU
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Chapter 3, Problem 3.37P
To determine

The acceleration of the center of mass aGx and the angular acceleration a.

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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.
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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

Chapter 3 Solutions

EBK SYSTEM DYNAMICS

Ch. 3 - The motor in Figure P3.11 lifts the mass mL by...Ch. 3 - Instead of using the system shown in Figure 3.2.6a...Ch. 3 - Consider the cart shown in Figure P3.13. Suppose...Ch. 3 - Consider the cart shown in Figure P3.13. Suppose...Ch. 3 - Consider the spur gears shown in Figure P3.15,...Ch. 3 - Consider the spur gears shown in Figure P3.15,...Ch. 3 - Derive the expression for the equivalent inertia...Ch. 3 - Prob. 3.18PCh. 3 - The geared system shown in Figure P3.19 represents...Ch. 3 - Prob. 3.20PCh. 3 - Prob. 3.21PCh. 3 - Prob. 3.22PCh. 3 - For the geared system shown in Figure P3.23,...Ch. 3 - For the geared system discussed in Problem 3.23,...Ch. 3 - The geared system shown in Figure P3.25 is similar...Ch. 3 - Consider the rack-and-pinion gear shown in Figure...Ch. 3 - The lead screw (also called a power screw or a...Ch. 3 - Prob. 3.29PCh. 3 - Derive the equation of motion of the block of mass...Ch. 3 - Assume the cylinder in Figure P3.31 rolls without...Ch. 3 - Prob. 3.33PCh. 3 - Prob. 3.34PCh. 3 - A slender rod 1.4 m long and of mass 20 kg is...Ch. 3 - Prob. 3.36PCh. 3 - Prob. 3.37PCh. 3 - The pendulum shown in Figure P3.38 consists of a...Ch. 3 - Prob. 3.39PCh. 3 - A single link of a robot arm is shown in Figure...Ch. 3 - 3.41 It is required to determine the maximum...Ch. 3 - Figure P3.42 illustrates a pendulum with a base...Ch. 3 - Figure P3.43 illustrates a pendulum with a base...Ch. 3 - 3.44 The overhead trolley shown in Figure P3.44 is...Ch. 3 - Prob. 3.45PCh. 3 - The “sky crane” shown on the text cover was a...
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