In terms of the s, s, 2s coordinates of a fixed space frame {s}, a frame...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
In terms of the s, ŷs, 2s coordinates of a fixed space frame {s}, a frame {a} has its &a-axis pointing in the direction (0, 0, 1) and its ŷa-axis pointing in the direction (-1,0,0), and a frame {b} has its -axis pointing in the direction (1,0,0) and its -axis pointing in the direction (0, 0, -1). Determine the following: (a) Draw by hand the three frames, at different locations so that they are easy to see. (b) Write down the rotation matrices Rsa and Rsb. (c) Given Rsb, determine Rwithout using a matrix inverse? (d) Given Rsa and Rsb, determine Rab. (e) Use Rsb to change the representation of the point p = (1,2,3) (which is in {b} coordinates) to {s} coordinates. (f) An angular velocity w is represented in {s} as ws = wa in {a}? (3, 2, 1). What is its representation (g) By hand, calculate the matrix logarithm [] of Rsa. Verify your answer with software, e.g. Matlab. Extract the unit angular velocity and rotation amount. Hint, check the three conditions of logarithm rotations from lecture slides L06. (h) Calculate the matrix exponential corresponding to the exponential coordinates of rotation A = (1,2,0). If using software, please provide a snapshot of your code. Hint, will be the norm of the [] product and the matrix exponential is given by R = e = I + sin 0 [w] + (1 - cos 0) [w] ². In terms of the s, ŷs, 2s coordinates of a fixed space frame {s}, a frame {a} has its &a-axis pointing in the direction (0, 0, 1) and its ŷa-axis pointing in the direction (-1,0,0), and a frame {b} has its -axis pointing in the direction (1,0,0) and its -axis pointing in the direction (0, 0, -1). Determine the following: (a) Draw by hand the three frames, at different locations so that they are easy to see. (b) Write down the rotation matrices Rsa and Rsb. (c) Given Rsb, determine Rwithout using a matrix inverse? (d) Given Rsa and Rsb, determine Rab. (e) Use Rsb to change the representation of the point p = (1,2,3) (which is in {b} coordinates) to {s} coordinates. (f) An angular velocity w is represented in {s} as ws = wa in {a}? (3, 2, 1). What is its representation (g) By hand, calculate the matrix logarithm [] of Rsa. Verify your answer with software, e.g. Matlab. Extract the unit angular velocity and rotation amount. Hint, check the three conditions of logarithm rotations from lecture slides L06. (h) Calculate the matrix exponential corresponding to the exponential coordinates of rotation A = (1,2,0). If using software, please provide a snapshot of your code. Hint, will be the norm of the [] product and the matrix exponential is given by R = e = I + sin 0 [w] + (1 - cos 0) [w] ².
Expert Answer:
Related Book For
Investment Analysis and Portfolio Management
ISBN: 978-0538482387
10th Edition
Authors: Frank K. Reilly, Keith C. Brown
Posted Date:
Students also viewed these mechanical engineering questions
-
Determine a suitable function f(x) and interval (a,b) to find -43 using Bisection Method with 6 steps. f(x)=...... a= b= Note: Use the table below to calculate the intervals and midpoints of...
-
Write the following trigonometric polynomials in terms of the basis functions (5.11): (a) cos2 a: (b) cos x sin x (c) sin3x (d) cos2 sin3x (e) cos4x
-
In terms of the "attract-retain-motivate" philosophy, how do benefits affect employee behavior?
-
Find the values of the parameter p > 0 for which the following series converge. k=1 k ^ ( + In k + 1/ P
-
Calculate the air-fuel ratio for the stoichiometric combustion of dodecane with 10% excess air, as shown in Fig. 12.22. Also determine the volume percentage of CO2 in the products, and the dew-point...
-
An oil company processes oil into aviation fuel and heating oil. It costs $65,000 to purchase each 1000 barrels of oil, which is then distilled and yields 500 barrels of aviation fuel and 500 barrels...
-
True or False: Multiple roots can exist when using IRR and MIRR methods.
-
Singer Company has a line of credit with United Bank. Singer can borrow up to $400,000 at any time over the course of the 2016 calendar year. The following table shows the prime rate expressed as an...
-
1. a) Suppose you deposit $2500 each year for 20 years in a savings account paying 5% compounded annually. How much would the account contain after 20 years? How much of the FV did you actually...
-
Carol Garcia is the bookkeeper for Sheridan Company. Carol has been trying to determine the correct balance sheet for Sheridan Company. Sheridan's balance sheet is shown below. SHERIDAN COMPANY...
-
All revenue accounts (totalling $600,000), expense accounts (totalling $650,000), and the Income Summary account have been closed for the year ended December 31, 2014 for Fineberg Productions, an...
-
Under IRC 467, his advance rental income received treated by the lessor for tax purposes? Is this income passive income?
-
(in thousands) Fraser Singh Travis Cash inflow (outflow) from operating activities $ 61,000 $ 53,000 $ (27,800) Cash inflow (outflow) from investing activities: Proceeds from sale of plant and...
-
3. It is mid-June 2021, and you are managing a portfolio of Japanese stocks that is benchmarked to the Nikkei 225 Index. You are concerned the Japanese stock market is heading for a downward...
-
How can you enhance my recommendation. To tackle this I propose lowering prices a bit: bakery items from $2.50 to $2.40, sandwiches from $3.25 to $3.20, and beverages $6.00 to $5.90. If we do this...
-
Develop audit criteria for undertaking an environmental audit of a manufacturer and supplier of fabrics to a company manufacturing clothes. Write 10-12 audit questions and state the required evidence...
-
Some management commenntators have argued that position or job descriptions are not necessary, that they are simply unneeded paperwork that occupy file space and they are not particularly useful. In...
-
Clark, PA, has been engaged to perform the audit of Kent Ltd.s financial statements for the current year. Clark is about to commence auditing Kents employee pension expense. Her preliminary enquiries...
-
Given the following balance sheet, fill in the ratio values for 2013 and discuss how these results compare with both the industry average and prior average performance of Sophie Enterprises. SOPHIE...
-
At the present time, you expect a decline in interest rates and must choose between two portfolios of bonds with the followingcharacteristics: Portfolio A Portfolio B 10.5 years 7% 5.7 years 125.18...
-
a. Someone in the 36 percent tax bracket can earn 9 percent annually on her investments in a tax-exempt IRA account. What will be the value of a one-time $10,000 investment in 5 years? 10 years? 20...
-
Bright Horizons Skilled Nursing Facility, an investor-owned company, constructed a new building to replace its outdated facility. The new building was completed on January 1, 2015, and Bright...
-
Great Forks Hospital reported net income for 2015 of \($2.4\) million on total revenues of \($30\) million. Depreciation expense totaled \($1\) million. a. What were total expenses for 2015? b. What...
-
What is the difference between long-term debt and current portions of long-term debt?
Study smarter with the SolutionInn App