1. In terms of the s, s, 2s coordinates of a fixed space frame {s}, the...

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1. In terms of the s, s, 2s coordinates of a fixed space frame {s}, the frame {a} has its a-axis pointing in the direction (0, 0, 1) and its a-axis pointing in the direction (1, 0, 0), and the frame {b} has its b-axis pointing in the direction (1, 0, 0) and its b-axis pointing in the direction (0, 0, -1). Draw the {s}, {a}, and {b} frames, similar to examples in the book and videos (e.g., Figure 3.7 in the book), for easy reference in this question and later questions. Write the rotation matrix Rsa. All elements of this matrix should be integers. 2. Referring to your drawing from Question 1, write Rb). All elements of this matrix should be integers. 3. Referring to your drawing from Question 1, write Rab. All elements of this matrix should be integers. 5. Referring back to Question 1, use Rsb to change the representation of the point p = (1,2,3) (in {b} coordinates) to {s} coordinates. All elements of this vector should be integers. 7. Referring back to Question 1, an angular velocity w is represented in {s} as ws representation wa? All elements of this vector should be integers. = (3, 2, 1)T. What is its 8. Referring back to Question 1, calculate the matrix logarithm [w]0 of Rsa by hand. (You may verify your answer with software.) Extract and enter the rotation amount in radians with at least two decimal places. 9. Calculate the matrix exponential corresponding to the exponential coordinates of rotation 0 = (1, 2, 0). The maximum allowable error for any matrix element is 0.01, so give enough decimal places where necessary. 10. Write the 3 x 3 skew-symmetric matrix corresponding to w = (1, 2, 0.5) T. Confirm your answer using the function VecToso3 in the given software. 1. In terms of the s, s, 2s coordinates of a fixed space frame {s}, the frame {a} has its a-axis pointing in the direction (0, 0, 1) and its a-axis pointing in the direction (1, 0, 0), and the frame {b} has its b-axis pointing in the direction (1, 0, 0) and its b-axis pointing in the direction (0, 0, -1). Draw the {s}, {a}, and {b} frames, similar to examples in the book and videos (e.g., Figure 3.7 in the book), for easy reference in this question and later questions. Write the rotation matrix Rsa. All elements of this matrix should be integers. 2. Referring to your drawing from Question 1, write Rb). All elements of this matrix should be integers. 3. Referring to your drawing from Question 1, write Rab. All elements of this matrix should be integers. 5. Referring back to Question 1, use Rsb to change the representation of the point p = (1,2,3) (in {b} coordinates) to {s} coordinates. All elements of this vector should be integers. 7. Referring back to Question 1, an angular velocity w is represented in {s} as ws representation wa? All elements of this vector should be integers. = (3, 2, 1)T. What is its 8. Referring back to Question 1, calculate the matrix logarithm [w]0 of Rsa by hand. (You may verify your answer with software.) Extract and enter the rotation amount in radians with at least two decimal places. 9. Calculate the matrix exponential corresponding to the exponential coordinates of rotation 0 = (1, 2, 0). The maximum allowable error for any matrix element is 0.01, so give enough decimal places where necessary. 10. Write the 3 x 3 skew-symmetric matrix corresponding to w = (1, 2, 0.5) T. Confirm your answer using the function VecToso3 in the given software.