**Problem 2: Coordinate Frame Analysis**In terms of the \( \hat{x}_s, \hat{y}_s, \hat{z}_s \) coordinates of a fixed space frame \(\{s\}\), frame \(\{a\}\) has its \( \hat{x}_a\)-axis pointing in the direction \((0, 0, 1)\) and its \( \hat{y}_a\)-axis pointing in the direction \((-1, 0, 0)\). Frame \(\{b\}\) has its \( \hat{x}_b\)-axis pointing in the direction \((1, 0, 0)\) and its \( \hat{y}_b\)-axis pointing in the direction \((0, 0, -1)\). The origin of \(\{a\}\) is at \((3, 0, 0)\) in \(\{s\}\) and the origin of \(\{b\}\) is at \((0, 2, 0)\) in \(\{s\}\).**Tasks:**(a) *Draw by hand a diagram showing \(\{a\}\) and \(\{b\}\) relative to \(\{s\}\).*(b) *Write down the rotation matrices \(R_{sa}\) and \(R_{sb}\) and the transformation matrices \(T_{sa}\) and \(T_{sb}\).*(c) *Calculate the matrix exponential corresponding to the exponential coordinates of rigid-body motion \(S \theta = (0, 1, 2, 3, 0, 0)\). Draw the corresponding frame relative to \(\{s\}\), as well as the screw axis \(S\).*

Answered: Image /qna-images/answer/fceb9180-0c2f-4745-9615-23ed5ea92bbe.jpg

Problem 2 In terms of the xs, ŷs, 2s coordinates of a fixed space frame {s}, frame {a} has its x-axis pointing in the direction (0, 0, 1) and its y-axis pointing in the direction (-1,0,0), and frame {b} has its x-axis pointing in the direction (1,0,0) and its ŷ₁-axis pointing in the direction (0,0,−1). The origin of {a} is at (3, 0, 0) in {s} and the origin of {b} is at (0, 2, 0) in {s}. (a) Draw by hand a diagram showing {a} and {b} relative to {s}. (b) Write down the rotation matrices Rsa and Rsb and the transformation matrices Tsa and Tsb.

Problem 2 In terms of the xs, ŷs, 2s coordinates of a fixed space frame {s}, frame {a} has its x-axis pointing in the direction (0, 0, 1) and its y-axis pointing in the direction (-1,0,0), and frame {b} has its x-axis pointing in the direction (1,0,0) and its ŷ₁-axis pointing in the direction (0,0,−1). The origin of {a} is at (3, 0, 0) in {s} and the origin of {b} is at (0, 2, 0) in {s}. (a) Draw by hand a diagram showing {a} and {b} relative to {s}. (b) Write down the rotation matrices Rsa and Rsb and the transformation matrices Tsa and Tsb.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

A cylindrical spaceship of length 35.0 m and diameter 8.35 m is traveling in the direction of its cylindrical axis (length). It passes by the Earth at a relative speed of 2.44××1088 m/s. a) What is the length of the ship, as measured by an Earth observer? b) What is the diameter of the ship, as measured by an Earth observer? c) How long does it take the spaceship to travel a distance of 10.0 km according to the ship's pilot? d) How long does it take the spaceship to travel a distance of 10.0 km according to an Earth-based observer?
The origins of two frames coincide at t = t' = 0 and the relative speed is 0.994c. Two micrometeorites collide at coordinates x = 118 km and t= 191 us according to an observer in frame S. What are the (a) spatial and (b) temporal coordinate of the collision according to an observer in frame S'? (a) Number i Units (b) Number i Units
Modern physics
The proper length of one spaceship is three times that of another. The two spaceships are traveling in the same direction and, while both are passing overhead, an Earth observer measures the two spaceships to have the same length. If the slower spaceship has a speed of 0.354c with respect to Earth, determine the speed of the faster spaceship. (Give your answer to at least 3 significant figures.) |c
Suppose 5 rocketships are all traveling in â in some frame S. The speeds are: St (min) 100 B 0 0.25 0.5 0.75 0.99 7 1 How much time passes on the clocks inside each rocketship if 100 minutes elapse on the stationary rocketship?
The space and time coordinates for two events as measured in a frame S are as follows: Event 1: x1=x0 , t1=x0/c Event 2: x2=2x0, t2=x0/2c a. There exists a frame in which these events occur at the same time. Find the velocity of this frame with respect to S. b. What is the value of t at which both events occur in the new frame?
All ans please
4
There is a lightbulb exactly halfway between the front and rear of a long hallway in your spaceship. Your ship is traveling at 0.5c relative to the earth. The bulb is suddenly turned on. Let event 1 be when the light from the bulb first strikes the front end of the hall, and event 2 be when it strikes the rear end. Which event occurs first, or are they simultaneous, in the frame of (a) the spaceship and (b) a person standing on the earth?
Suppose two angry rhinoceros charge each other. According to a few observers on the ground, the rhinoceros on the left moved to the right at a speed of (1 - ϵ)c while the rhinoceros on the right moved to the left at a speed of (1 - ϵ)c. ϵ is in the range of 0 < ϵ < 1. How fast is the rhinoceros on the right moving in the frame of the rhinoceros on the left? (Show that this speed is less than c, no matter how small ϵ is)
Chapter 37, Problem 015 The center of our Milky Way galaxy is about 24000 ly away. (a) To eight significant figures, at what constant speed parameter would you need to travel exactly 24000 ly (measured in the Galaxy frame) in exactly 27 y (measured in your frame)? (b) Measured in your frame and in lightyears, what length of the Galaxy would pass by you during the trip? (a) Number Units (b) Number Units
A frame B shown below in Figure 1, is rotated 90° about the z-axis, then translated 3 and 5 units relative to the n- and o-axis respectively, then rotated another 90° about the n-axis, and finally, 90° about the y-axis. Find the new location and orientation of the frame. (1,1,2) {B} F y a Figure 1 11