AEE 4263 HW 10

.docx

School

Florida Institute of Technology *

*We aren’t endorsed by this school

Course

4263

Subject

Mechanical Engineering

Date

Apr 3, 2024

Type

docx

Pages

5

Uploaded by LieutenantNeutron10368 on coursehero.com

AEE 4263-02 Space Flight Mechanics Homework HW10 Fall 2023 1. (15 points) A spacecraft has the following inertia tensor: I = [ 500 − 8 − 7 − 8 300 − 5 − 7 − 5 400 ] kg − m 2 a. (5 points) What are the minimum, intermediate, and maximum principal moments of inertia to the nearest kg − m 2 ? b. (10 points) What is the transformation matrix from body to principal coordinates (i.e., C b p ) to four decimal places? Solution: a. Minimum MOI= 501 kg − m 2 Intermediate MOI= 400 kg − m 2 Maximum MOI= 299 kg − m 2 b. C b p = -0.9970 -0.0416 -0.0652 0.0380 -0.9978 0.0551 0.0674 -0.0525 -0.9963 MATLAB: %% Homework 10 Problem 1 close all clear all clc I= [500 -8 -7; -8 300 -5; -7 -5 400] %kg-m^2 [eigenVectors, eigenValues] = eig(I) I_pricipal= [-eigenVectors(:,3), eigenVectors(:,1), eigenVectors(:,2)] I_pricipal'*I*I_pricipal; MOI= diag(eigenValues) 1
2. (15 points) A spacecraft is spinning about the z-axis of its principal frame at 2 π rad / s . The principal moments of inertia about the center of mass are: I xx = 370 kg − m 2 I yy = 420 kg − m 2 I zz = 530 kg − m 2 The nutation damper has the following properties: R = 1 m μ = 0.01 m = 10 kg k = 10000 N / m c = 150 N − s m Use the Routh Hurwitz stability criteria to assess the spacecraft’s stability as a: a. (7 points) major axis spinner b. (7 points) minor axis spinner c. (1 point) why do you not need to evaluate the intermediate axis? Solution: a. Major axis = Stable r1_maj =1538460 r2_maj =23859450 r3_maj =1588940954.55 r4_maj =134666.21 r5_maj =7361318631.66 b. Minor axis = Unstable r1_min =2203740 r2_min =34177050 r3_min =2276680293.88 r4_min =-149591.50 r5_min =2970492893.22 c. Intermediate axis: Did not need to evaluate because motion is not stable by there being different signs on the r’s. Spin is unstable about the intermediate axis. r1_int =1941390 r2_int =29964450 r3_int =1996576766.15 r4_int =-231592.44 r5_int =-2584430101.53 MATLAB: %% Homework 10 Problem 2 close all clear all clc R= 1; %m mu= 0.01; m= 10; %kg k= 10000; %N/m c= 150; %N-s/m w0= 2*pi; % Major 2
Ixx_maj= 370; %kg-m^2 Iyy_maj= 420; %kg-m^2 Izz_maj= 530; %kg-m^2 MOI_maj= [Ixx_maj Iyy_maj Izz_maj]; a4_maj= (1-mu)*m*Ixx_maj*Iyy_maj; a3_maj= c*Ixx_maj*(Iyy_maj+ (1-mu)*m*R^2); a2_maj= k*(Iyy_maj+(1-mu)*m*R^2)*Ixx_maj + (1-mu)*m*((Ixx_maj- Izz_maj)*(Iyy_maj-Izz_maj)-(1-mu)*Ixx_maj*m*R^2)*w0^2; a1_maj= c*((Ixx_maj-Izz_maj-(1-mu)*m*R^2)*(Iyy_maj-Izz_maj))*w0^2; a0_maj= k*((Ixx_maj-Izz_maj-(1-mu)*m*R^2)*(Iyy_maj-Izz_maj))*w0^2 + ((Iyy_maj-Izz_maj)*(1-mu)^2)*m^2*R^2*w0^4; r1_maj= a4_maj r2_maj= a3_maj r3_maj= a2_maj-((a4_maj*a1_maj)/a3_maj) r4_maj= a1_maj- (a3_maj^2 *a0_maj)/((a3_maj*a2_maj) - (a4_maj*a1_maj)) r5_maj=a0_maj % Minor Ixx_min= 530; %kg-m^2 Iyy_min= 420; %kg-m^2 Izz_min= 370; %kg-m^2 MOI_min= [Ixx_min Iyy_min Izz_min]; a4_min= (1-mu)*m*Ixx_min*Iyy_min; a3_min= c*Ixx_min*(Iyy_min+ (1-mu)*m*R^2); a2_min= k*(Iyy_min+(1-mu)*m*R^2)*Ixx_min + (1-mu)*m*((Ixx_min- Izz_min)*(Iyy_min-Izz_min)-(1-mu)*Ixx_min*m*R^2)*w0^2; a1_min= c*((Ixx_min-Izz_min-(1-mu)*m*R^2)*(Iyy_min-Izz_min))*w0^2; a0_min= k*((Ixx_min-Izz_min-(1-mu)*m*R^2)*(Iyy_min-Izz_min))*w0^2 + ((Iyy_min-Izz_min)*(1-mu)^2)*m^2*R^2*w0^4; r1_min= a4_min r2_min= a3_min r3_min= a2_min-((a4_min*a1_min)/a3_min) r4_min= a1_min- (a3_min^2 *a0_min)/((a3_min*a2_min) - (a4_min*a1_min)) r5_min=a0_min % Intermediate Ixx_int= 370; %kg-m^2 Iyy_int= 530; %kg-m^2 Izz_int= 420; %kg-m^2 MOI_int= [Ixx_int Iyy_int Izz_int]; a4_int= (1-mu)*m*Ixx_int*Iyy_int; a3_int= c*Ixx_int*(Iyy_int+ (1-mu)*m*R^2); a2_int= k*(Iyy_int+(1-mu)*m*R^2)*Ixx_int + (1-mu)*m*((Ixx_int- Izz_int)*(Iyy_int-Izz_int)-(1-mu)*Ixx_int*m*R^2)*w0^2; a1_int= c*((Ixx_int-Izz_int-(1-mu)*m*R^2)*(Iyy_int-Izz_int))*w0^2; a0_int= k*((Ixx_int-Izz_int-(1-mu)*m*R^2)*(Iyy_int-Izz_int))*w0^2 + ((Iyy_int-Izz_int)*(1-mu)^2)*m^2*R^2*w0^4; 3
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Related Questions
Edition Eighth Z▼▲ Ā Mc Graw Hill Vector Mechanics for Engineers: Statics HW: Ch 6 จงหาตำแหน่งของจุดศูนย์ถ่วงของชิ้นส่วนเครื่องจักรกลด้านแกน x ของวัสดุประกอบดังรูป Find the position of the center of gravity of the mechanical part on the x-axis side of the composite as shown in the figure. mm 20 34 mm 62 mm 51 mm 20 mm 200 mm 10 mm © 2007 The McGraw-Hill Companies, Inc. All rights reserved. 45 m 100 mm 55 mm 7-52
A mechanic changing a tire rolls a wheel along the ground towards the car. The radius of the wheel is 42cm, and the speed of the wheel as it rolls is 2 revolutions per second. Height Above Ground (m) radiu HIDE wheel spet Time The diagram above illustrates the vertical motion of a point on the tire over time. It is possible to model the height of this point using a sinusoidal function of the form h(t)=-a sin[b(t-c)]+d. a) Determine the length of time required for one revolution of the tire. b) State the numerical value for each of the parameters a, b, c & d. And write a function representing the motion of the point in the form h(t)= -a sin[b(t−c)]+d.
Saved em Set 02 - Chapter 2 Part 1 Required information of 2 Consider the following vectorial representations. Add the three vectors shown to form a resultant vector R , and report your result using polar vector representation. Take Y= 3 m. 2 m ok 3 m 30° 162 2 (Enter a positive value for the phase angle.) 4.84 m @ ces
ihài 25 Q3) Let vector A = 5i +2j, Vector B = -3i %3D -5j, and vector C = A+ B. (a) Write %3D vector C in component form. (b) Draw a coordinate system and on it show the all vectors. (c) What are the ?magnitude and direction of vector C
36- O A) 30 i- 19 k Nm B) 30 i+9k Nm C) 30 j-9k Nm O D) 12i+30j-9k Nm O E) 9j+30 k Nm
force 15[kN-m¹] JUN JUL A 2m. 2m 2m 7x incl 25[KN) Find location of the application of the resultant to generate the proper moment of force about 0. Ge
For the Following question Graph all 4 : [I just need all 4 graphs and please explain and make clean solution] Position vs time Velocity vs time Acceleration vs time Force vs time [For your convenience, I have solved the numerical solutions for the problem] (Please Look at the picture since it is much cleaner) Question : A 550 kilogram mass initially at rest acted upon by a force of F(t) = 50et Newtons. What are the acceleration, speed, and displacement of the mass at  t = 4 second ? a =(50 e^t)/(550 ) [N/kg] v = ∫_0^t▒(50 e^t )dt/(550 )= v_0  +(50 e^t-50)/550=((e^t- 1))/11 x = ∫_0^t▒(e^t- 1)dt/(11 )= x_0  +(e^t- t - 1)/(11 ) a(4s)=(50*54.6)/550= 4.96[m/s^2 ] v(4s)=((e^4-1))/11= 4.87[m/s] x(4s)=((e^4- 4 - 1))/11= 4.51 [m]
m and n are orthogonal vectors. Let their component forms be defined as (mx, my) and (nx, ny) respectively, where all values are integers. mx+nx=-3 and nymy=40. If O
Which of the following dimensions belongs in the set (force, velocity, acceleration, magnetic field}? * mass speed displacement temperature When two vectors are perpendicular, their * dot product is zero cross product is zero. both are zero both are not necessarily zero The cross product of tWO vectors 3İ + 4j -5k and-i+j- 2k is
A docs.google.com In circular motion vr=0 vr=v theta vr=-v theta ar=0 The right representation of r-theta ***I' coordinates is --- a b. d a O b According to the figure, the vector 25 points equation is
10. [-/3 Points] DETAILS SERCP8 4.P.012. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Two forces are applied to a car in an effort to move it, as shown in the following figure, where F, = 427 N and F, = 381 N. (Assume up and to the right as positive directions.) 10° 180° F (a) What is the resultant of these two forces? magnitude N direction ° to the right of the forward direction (b) If the car has a mass of 3,000 kg, what acceleration does it have? Ignore friction. m/s2 Need Help? Read It
Can you answer quickly 9)Let A axis team consist of XA, YA and ZA vectors, and B axis team consists of vectors XB, YB and ZB. Let the expression of the origin of the A axis set on the B axis set be denoted by BPAORG. Let BVA denote the representation of the vector VA on the B axis set. Let it be defined as BAR = [BXA BYA BZA]. BAR BPAORG0 0 0 1 Let the 4x4 matrix given as BAT. So what is the result of BAT ACT CBT matrix multiplication? Matrix whose diagonal elements are zero and whose other elements are aZero matrixMatrix whose all elements are oneIdentity matrix
Q4/B/ the value of X-bai Q4/ For the figure below, all 0.987 dimensions in inch. A/The total O 2.5 Area : * O 0.857 O 0.254 y 0.398 O 1.06 1.5 O 2 0.65 2.5 0.5 2.5 O 0.487 0.55 2.5 2.5 Other: 3.
It's shown in Fig. 1 that the coordinate frame 0₁X₁Y₁Z₁ is oriented at an angle 0 = 30° with respect to 0oXoyozo, and p¹ = []. Find rotation matrices R and R, and show that RR = 1, where I is an identity matrix. F3 49 F4 H ------- % Yo 00, 01 H Q Search F5 p Q cos A 6 F6 8=30° ** F7 & 7 -40 sin 0 PrtScn F8 Home H F9 End F10 PgUp F
Fill in each of the following blanks with the appropriate word: If the displacement model used in the derivation of the element stiffess matrices is also used to derive the element mass matrices, the resulting mass matrix is called __ mass matrix.
V-axis X-axis A Figure 1. An object (yellow point) travels from point A to point B along the arc of a circle that is centered at point O (red point). velocity of an object, either due to a change in speed or direction, means the object is accelerating. According to Newton's second law, an object will accelerate only if there is a non-zero total force acting on the object. For uniform circular motion, it turns out that this force must always be pointing towards the center of the circle that the object is travelling around and we say that there is a centripetal force present. You can use Newton's second law and a little bit of geometry to understand why an object undergoing uniform circular motion must be experiencing a force that is pointing towards the center of the circle the object is travelling on. If the acceleration vector pointed above or below the plane of the circle, the velocity vector would also end up pointing out of the plane that the circle is on. Since the velocity vector…
Resolve for the x and y component of F3. y F3%3D650 N 3) F, = 750 N %3D 45° F = 900 N X component of F3: [Choose] y component of F3: [ Choose ]
A four-bar mechanism is used to transmit power to slider E. Link AC rotates counterclockwise at 100 rpm. A and B are fixed points. The following linkages are measured in cm: AC=35, AB=70, CD=45, BD=45, DE=40. Find the instantaneous velocity of slider E in cm/s 1.Draw the mechanism in appropriate scale on your paper2. Find the instantaneous linear velocity of C3. Find a point on your paper to draw the velocity polygon and scale the magnitude of the computed linearvelocity4. Use the relative velocity equation for finding the linearvelocity of D; ? = ? + ?? ? ?/?5. Remember that although the magnitudes are unknown, their directions can be identified6. Obtain the magnitudes of the unknown velocities from the velocity polygon7. For Link DE, repeat the process by using ? = ? + ??the line as much as needed8. Remember that E is a SLIDER therefore it can only goin the direction where its movement is not constrained? . Add the vector ? to the head of ? and extend?/? ?/??
Two cables AB and AC are acting on the pole with forces FAB = 740N and FAC = 540N with parameters defining the attachment points shown in the table. We want to write the vector FAB in cartesian vector form. A FAC FAB L X2 Y2 Y1 X1 В parameters value units FAB FAC 740 N 540 N L 7 3.5 m 4 m Write the vector FAR in Cartensian Vector Notation. АВ Round your final answers to 3 significant figures. FAB = i + j+ 524
Classwork for PHYS220-A-Ali Sabbah-SP2021 Beirut Sec-A Beirut (MW 09:30-10:45) google.com/u/0/w/Mjc5NTQzMDc5NTgz/t/all PHYS220 Spring/20-21 Practice Sheet-1 Keys 1) A0.1 kg object oscillates as a s At a position X,, the object has a kinetic energy of 0.7 J and a potential energy 0.3 J. The amplitude of oscíllation, A, is: (a) 0.12 m (b) 0.22 m aple harmonic motion along the x -axis with a frequency f 3.185 Hz. (c) 0.31 m (d)0.42 m EJE the
After the web meeting, submit this document on Canvas Undel ne Meeting Assignment. This is an individual submission. TAE %3D Follow the steps below to express the force F, as a vector using the format: F, = F 1. Write the position vector: TAE = 4 ft 4 ft F = 300 lb 6 ft 6 ft 2. Find the magnitude of the position vector: 6 ft TAE = F = 400 lb 3. Find the unit vector by dividing the position vector by its own magnitude: NAE = 4. Write the force vector: F1 =FinAE =
Given frames {A}, {B} and {C} as shown below, find transformation matrix from B to A, and from C to A. 30° Yc 60 ZA 2 units YA ZB XA YB 3 units
Consider for the part in the figure below, a = 106, b =60 and c =112. 80 20 45 Dimensions in mm Analyze the part in order to calculate the coordinates of the centre of gravity in the (r, y, z) system of coordinates. It is assumed that the following process was following for the manufacturing process • Part 1(a cubic piece of dimension 51 x 60 x 60 is cut out of a Part 2 of dimensions 157 x 60 x 80 and then • Part 3 (triangular prism) is welded Part 2 Fill inN K IA with coordinates of centers of respective parts in mm Yi Vi
Two cables AB and AC are acting on the pole with forces FAB = 540N and FAC = 560N with parameters defining the attachment points shown in the table. We want to write the vector FAB in cartesian vector form. C X Y₂ parameters value units FAB 540 FAC 560 L ZI 3 7₂ 5.5 4 3.5 4 4 Submit Question N N m m m m m FAC A Y₁ Z write the vector FAB in Cartensian Vector Notation. Round your final answers to 3 significant figures. FAB= AB B L X1 N
Name ASsignment ES MTH 175 (Cameron) 8.4 Vector Models Tutoring Assistance Permitted #17. An airplane has an airspeed of 884 kilometers per hour bearing N53°E. The wind velocity is 66 km/hour in the direction of N38°W. a) Write vectors (to the nearest tenth) representing the airplane A, the 884 km/hr wind W, and the aircraft relative to the ground R. 66 km/hr 389 1532 A = W R
An object of mass m is being affected by the force F = cxx, where c is a positive constant. The object leaves the origin with a speed i, at timet = 0. Find x(x). Answer to Question 1 [Insert solution image after this line]: %3D %3D
3-D Model the following angle tab part. Unit system: MMGS (millimeter, gram, second) Part origin: as specified (center of hole) Material: 6061 Alloy 170 R O a. 1280.91 grams O b. 1593.72 grams O c. 1147.25 grams O d. 1398.47 grams 3 8x 45 80 960- R20 Origin What is the overall mass of the part? 116 156 13 040 8x as -2x @ 15
[36] j[24] k[54] Define the unit vector between the 2 points in the form of (#i,#j,#k) (Round to two significant figures)
Match 4 correct pairs between List-l and List-ll for questions. No credit will be given for partially correct matching. List-l A. Collision of particles B. Stability C. Satellite motion D. Spinning top List-ll 1. Euler's equation of motion 2. Minimum kinetic energy 3. Minimum potential energy 4. Impulse momentum principle 5. Conservation of moment of momentum
" Centroids " from the Book Engineering Mechanics  Statics and Dynamics by Ferdinand Singer. I think the solution is like the one in the second picture, i just cannot get the right answer in the answer key given please help me thankyou! I think the one that is in the answer key was the Xbar (X̅) and Ybar ( ȳ ).
Command: PLOTTERMANAGER (from the autocad file m TO CONFIGURE A LOCAL, NONSYSTEM PLOTTER 10. PROFILES-Controls the use of profiles. A profile is a configuration you define. 367N 367N R=1.0m 426N 426N B. 426N C. The two identical sphemes having oqual weights of 367N is placed on top of the three identic al sphere's w/ 426 N as their reight . Compute the reaction A,B and C
Engineering Mechanics ( Statics: Resultant 3D )
Use of Infinite Sequences and Series in Problem Solving of Special Theory of Relativity.  A spacecraft travels fast the earth has a greater velocity (ⱱ) which approximates the speed of light. The time (to) measured in the spacecraft is different from the time (t) measured on earth. The time difference is given, to = t √1- ⱱ 2/c2 = t (1 – ⱱ 2/c2)1/2.
HW_5_01P.pdf PDF File | C:/Users/Esther/Downloads/HW_5_01P.pdf 2 Would you like to set Microsoft Edge as your default browser? Set as default To be most productive with Microsoft Edge, finish setting up your Complete setup Maybe later browser. (D Page view A Read aloud V Draw 7 Highlight 2 of 3 Erase 5. Two cables are tied to the 2.0 kg ball shown below. The ball revolves in a horizontal circle at constant speed. (Hint: You will need to use some geometry and properties of triangles and their angles!) 60° 1.0 m 60° © 2013 Pearson Education, Inc. (a) For what speed is the tension the same in both cables? (b) What is the tension? 2. 2:04 PM O Type here to search C A 2/9/2021 (8)
Find the standard equation of the sphere with the given characteristics. Center: (-1, -6, 9) Radius: 7 еВook Submit Answer View Previous Question Question 2 of 7 View Next Question Home My Assignments O Request Extension P Type here to search A 31°C 10:44 AM 22-Oct-2 not m esc 17 12/A prt sc delete 23 2 3 4 8. tab Q W R Y U OF A S G H. J K L caps lock shift& C fn + esc alt 目 ctrl ctrl fn alt 6
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Text book image
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Text book image
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Text book image
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Text book image
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Text book image
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
SEE MORE TEXTBOOKS
Related Questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Text book image
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Text book image
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Text book image
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Text book image
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Text book image
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
SEE MORE TEXTBOOKS