The initial (3-2-1) Euler angles yaw, pitch and roll of a vehicle are (1), 0, 0) = (40, 30, 80) degrees. Assume the body angular velocity vector of the craft is given through the B frame components as Bw= sin(0.1t)] 0.01 20deg/s. Write a program to numerically integrate the yaw, pitch and roll angles over [cos(0.1t). a simulation time of 1 minute. Enter the Euler angle norm √№2 +0² + 02 at the simulation time step 42s. Express angles in radians. Let the initial angles integrate, don't wrap them to any particular quadrants.

The initial (3-2-1) Euler angles yaw, pitch and roll of a vehicle are (1), 0, 0) = (40, 30, 80) degrees. Assume the body angular velocity vector of the craft is given through the B frame components as Bw= sin(0.1t)] 0.01 20deg/s. Write a program to numerically integrate the yaw, pitch and roll angles over [cos(0.1t). a simulation time of 1 minute. Enter the Euler angle norm √№2 +0² + 02 at the simulation time step 42s. Express angles in radians. Let the initial angles integrate, don't wrap them to any particular quadrants.

C++ for Engineers and Scientists

4th Edition

ISBN:9781133187844

Author:Bronson, Gary J.

Publisher:Bronson, Gary J.

Chapter5: Repetition Statements

Section: Chapter Questions

Problem 2PP: (Mechanics) The deflection at any point along the centerline of a cantilevered beam, such as the one...

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(Mechanics) The deflection at any point along the centerline of a cantilevered beam, such as the one used for a balcony (see Figure 5.15), when a load is distributed evenly along the beam is given by this formula: d=wx224EI(x2+6l24lx) d is the deflection at location x (ft). xisthedistancefromthesecuredend( ft).wistheweightplacedattheendofthebeam( lbs/ft).listhebeamlength( ft). Eisthemodulesofelasticity( lbs/f t 2 ).Iisthesecondmomentofinertia( f t 4 ). For the beam shown in Figure 5.15, the second moment of inertia is determined as follows: l=bh312 b is the beam’s base. h is the beam’s height. Using these formulas, write, compile, and run a C++ program that determines and displays a table of the deflection for a cantilevered pine beam at half-foot increments along its length, using the following data: w=200lbs/ftl=3ftE=187.2106lb/ft2b=.2fth=.3ft
(Statics) An annulus is a cylindrical rod with a hollow center, as shown in Figure 6.7. Its second moment of inertia is given by this formula: I4(r24r14) I is the second moment of inertia (m4). r2 is the outer radius (m). r1 is the inner radius (m). a. Using this formula, write a function called annulusMoment ( ) that accepts two double-precision numbers as parameters (one for the outer radius and one for the inner radius), calculates the corresponding second moment of inertia, and displays the result. b. Include the function written in Exercise 5a in a working program. Make sure your function is called from main(). Test the function by passing various data to it.
(Practice) Determine names for functions that do the following: a. Find the average of a set of numbers. b. Find the area of a rectangle. c. Find the minimum value in a set of numbers. d. Find the density of a steel door. e. Sort a set of numbers from lowest to highest
(Program) Write a program that tests the effectiveness of the rand() library function. Start by initializing 10 counters, such as zerocount, onecount, twocount, and so forth, to 0. Then generate a large number of pseudorandom integers between 0 and 9. Each time 0 occurs, increment zerocount; when 1 occurs, increment onecount; and so on. Finally, display the number of 0s, 1s, 2s, and so on that occurred and the percentage of time they occurred.
(Statics) A beam’s second moment of inertia, also known as its area moment of inertia, is used to determine its resistance to bending and deflection. For a rectangular beam (see Figure 6.6), the second moment of inertia is given by this formula: Ibh3/12 I is the second moment of inertia (m4). b is the base (m). h is the height (m). a. Using this formula, write a function called beamMoment() that accepts two double- precision numbers as parameters (one for the base and one for the height), calculates the corresponding second moment of inertia, and displays the result. b. Include the function written in Exercise 4a in a working program. Make sure your function is called from main(). Test the function by passing various data to it.
(General math) a. Write a C++ program to calculate and display the value of the slope of the line connecting two points with the coordinates (3,7) and (8,12). Use the fact that the slope between two points with the coordinates (x1,y1)and(x2,y2)is(y2y1)/(x2x1). b. How do you know the result your program produced is correct? c. After verifying the output your program produces, modify it to determine the slope of the line connecting the points (2,10) and (12,6). d. What do you think will happen if you use the points (2,3) and (2,4), which results in a division by zero? How do you think this situation can be handled? e. If your program doesn’t already do so, change its output to this: The value of the slope is xxx.xx The xxx.xx denotes placing the calculated value in a field wide enough for three places to the left of the decimal point and two places to the right of it.
Find the error(s) in the following code: (6)
(Heat transfer) The formula developed in Exercise 5 can be used to determine the cooling time, t, caused only by radiation, of each planet in the solar system. For convenience, this formula is repeated here (see Exercise 5 for a definition of each symbol): t=Nk2eAT3fin A=surfaceareaofasphere=4r2 N=numberofatoms=volumeofthespherevolumeofanatom Volume of a sphere sphere=43radius3 The volume of a single atom is approximately 11029m3 . Using this information and the current temperatures and radii listed in the following chart, determine the time it took each planet to cool to its current temperature, caused only by radiation.
(Computation) Among other applications, Pascal’s triangle (see Figure 7.22) provides a means of determining the number of possible combinations of n things taken r at a time. For example, the number of possible combinations of five people (n = 5) taken two at a time (r=2)is10. Each row of the triangle begins and ends with 1. Every other element in a row is the sum of the element directly above it with the element to the left of the one above it. That is, element[n][r]=element[n1][r]+element[n1][r1] Using this information, write and test a C++ program to create the first 11 rows of a twodimensional array representing Pascal’s triangle. For any given value of n less than 11 and r less than or equal to n, the program should display the correct element. Use your program to determine in how many ways a committee of 8 can be selected from a group of 10 people
(Debug) Determine and correct the errors in the following programs. a.includeiostreamusingnamespacestd;intmain()width=15area=lengthwidth;coutTheareaisareab.includeiostreamusingnamespacestd;intmain()intlength,width,area;area=lengthwidth;length=20;width=15;coutTheareaisarea;return0;c.includeiostreamintmain()intlength=20;width=15,area;lengthwidth=area;coutTheareais,area;return0;
(Useful utility) Modify the program written for Exercise 3 to search for the first occurrence of a user-entered sequence of characters, and then replace this sequence, when it’s found in the string, with a second user-entered sequence. For example, if the entered string is Figure 4-4 illustrates the output of Program 4-2 and the user enters that 4- is to be replaced by 3-, the resulting string is Figure 3-4 illustrates the output of Program 4-2. (Only the first occurrence of the searched-for sequence has been changed.)
(Automotive) a. An automobile engine’s performance can be determined by monitoring its rotations per minute (rpm). Determine the conversion factors that can be used to convert rpm to frequency in hertz (Hz), given that 1rotation=1cycle,1minute=60seconds,and1Hz=1cycle/sec. b. Using the conversion factors you determined in Exercise 7a, convert 2000 rpm into hertz.