Problem: Lagrangian and Eulerian DescriptionThe motion of a body is given byX = X, +aX,tx, = X, +aX,tx; = X;with a constantwith (x1, x2, X3) being the coordinates of a material point M in the current configuration at a time"t", while (X1, X2, X3) are the coordinates at t=0 (initial configuration)a) Determine the displacement vector u(X1, X2, X3), the velocity vector v(X1, X2, X3) in theLagrangian description.b) Determine the displacement vector u(x1, x2, X3), the velocity vector v(x1, X2, X3) in theEulerian description.ôx,c) Calculate the deformation gradient F (F,).d) Calculate the right Cauchy Green strain tensor C and the finite strain tensor E

Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Answered: The motion of a body is given by X; =…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

2. A kilogram mass is attached to the end of the spring with spring constant 2 N/m. Find the equation of motion if the mass is initially released (set in motion) from rest from a point 1 meter above equilibrium position. (Use the convention that displacements measured below the equilibrium position are positive.) (a) Write the initial-value problem which describes the position of the mass. (b) Find the solution to your initial-value problem from part (a). (c) Graph the solution found in (b) on (0
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 =
2. Solve the system linear of Equation using Gauss- Jordan elimination (row operations), find the value of x1, x2 and x3. 2X1 - 2X2 + X3 = 3 3X1 - X3 + X2 = 7 X1 - 3X2 + 2X3 = 0
Consider the following vector: • J= 17 @ 195° What is the x component of J? 17 @ 195° 16.42 @ 90° 17 @ 15° O 17 @ 180° (10, 16.42) O -16.42 @ 180° (0,17) 16.42 @ 180° 16.42 @ 0° 16.42 @ 195° 16.42 @ 15° O (17,0)
A point P is located at (0 0 100) in a body coordinate frame. If the rigid body rotates 60deg about the global X-axis and the origin of the body translates to (X, Y, Z)=(500, 0 600), find the final position (X2, Y2, Z2) in the Global frame by using 4X4 matrix.
Find the transformation matrix for the following rotations: 1) Rotate a about the original x-axis (in frame 0). (Xo, Yo, Zo) → (X₁,Y₁,Z₁); 2) Followed by a rotation of B about current z-axis (in frame 1). (X₁,Y₁,Z₁)→ (X₂, X₂, Z₂); 3) Followed by a rotation of y about Xo -axis (in frame 0). (X2, Y, Z₂)→ (X3, Y, Z3); 4) Followed by a rotation of about Z3 - axis (in frame 3). (X3, X3,Z3) → (X,Y4, Z4). E F3 $ R F F4 Q Search DII % 5 F5 T F6 6 Y PRE F7 & H 7 PrtScn F8 U 8 Home End
Consider the manipulator provided in the figure. Given the Position vector P w.r.t. to the base frame, derive the Analytical Jacobian for the position. Write your answer as J = [dpx/dq1 dpx/dq2 dpx/dq3; dpy/dq1 dpy/dq2 dpy/dq3; dpz/dq1 dpz/dq2 dpz/dq3] %3D Z3, Z4 Z1, Y, b,s, +b;C;82 -b,c +b3S152 -b;C2 X4 YA #3 b2 b3 O2, 02 P = #2 Z, Y3 #0
Find a vector x whose image under T, defined by T(x) = Ax, is b, and determine whether x is unique. Let 1 3 6 15 4 15 27 69 0 1 1 -4 - 13 - 25 A= b= x= 3 - 63 Find a single vector x whose image under T is b. s the vector x found in the previous step unique? O A. Yes, because there are no free variables in the system of equations. O B. Yes, because there is a free variable in the system of equations. O C. No, because there are no free variables in the system of equations. O D. No, because there is a free variable in the system of equations.
$+2.5$41 543834 2 8 b. A student has written a mathematical model for a rotational mechanical system without gears and some data were missing as shown below: [4s² + 2s +5 -25 as 0 -2s 3s² + 4s +6 -(1+B) 0 -6 3s +6 [0₁(s)] 0₂ (s 03(s)] What are the values of a and B? 2. What is the degree of freedom of the system? Sketch the expected rotational mechanical system and show thetorque, angular displacements and all values of inertias, springs, and dampers on the sketch with 85²2445445+8 their units. (89² +2+5+8) (33+4)
Learning Goal: To use the dot product to find the components of forces acting in arbitrary directions. A three-legged structure is shown below. It is attached to the ground at points B= (4.68,0,0) and C=(-4.68.0.0) and connected to the ceiling at point A = (-5.54,3.10.4.47). The three legs connect at point D = (0,2.49, 4.00). where two forces, F and P. act. Force F is given by F= 6.00 i 12.5j + 26.2 k N: P has Figure 1 of 1 D Important: If you use this answer in later parts, use the full unrounded value in your calculations. ▾ Part D - Finding the component of a force perpendicular to a direction Given F 6.00 i 12.5j +26.2 kN, find the component of F that acts perpendicular to member DA such that the vector addition of the perpendicular and parallel components of F (F=F+F) with respect to DA equals F. Express your answer in component form. Express your answers, separated by commas, to three significant figures. View Available Hint(s) FIDA Submit VAXtvec Previous Answers * Incorrect;…
The position vector rAB = 150i – 85j + TAB2 k has magnitude equal to 188 m. a) Determine the z-component r48 2 (positive). b) If the coordinates of point A are (25, 50, -20)m, define the coordinates of point B. c) Find the angle in degrees of the vector with the y-axis. d) Express a unit vector parallel to rAB in terms of components.
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

SEE MORE QUESTIONS

Recommended textbooks for you

Elements Of Electromagnetics

Mechanical Engineering

ISBN:

9780190698614

Author:

Sadiku, Matthew N. O.

Publisher:

Oxford University Press

Mechanics of Materials (10th Edition)

Mechanical Engineering

ISBN:

9780134319650

Author:

Russell C. Hibbeler

Publisher:

PEARSON

Thermodynamics: An Engineering Approach

Mechanical Engineering

ISBN:

9781259822674

Author:

Yunus A. Cengel Dr., Michael A. Boles

Publisher:

McGraw-Hill Education

Elements Of Electromagnetics

Mechanical Engineering

ISBN:

9780190698614

Author:

Sadiku, Matthew N. O.

Publisher:

Oxford University Press

Mechanics of Materials (10th Edition)

Mechanical Engineering

ISBN:

9780134319650

Author:

Russell C. Hibbeler

Publisher:

PEARSON

Thermodynamics: An Engineering Approach

Mechanical Engineering

ISBN:

9781259822674

Author:

Yunus A. Cengel Dr., Michael A. Boles

Publisher:

McGraw-Hill Education

Control Systems Engineering

Mechanical Engineering

ISBN:

9781118170519

Author:

Norman S. Nise

Publisher:

WILEY

Mechanics of Materials (MindTap Course List)

Mechanical Engineering

ISBN:

9781337093347

Author:

Barry J. Goodno, James M. Gere

Publisher:

Cengage Learning

Engineering Mechanics: Statics

Mechanical Engineering

ISBN:

9781118807330

Author:

James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher:

WILEY

SEE MORE TEXTBOOKS