Consider a reference frame N comprising a set of unit vectors nx, ny, and nz. A vector v has the form: V = xnx + znz, where x and z are scalar constants. a. Express this vector in a new reference frame E, which is obtained by a positive rotation about the ny. Store your answer in a variable named v_final. b. Consider now the effect of a second rotation, 0, about the x-direction of the frame E, which results in a new frame F. What is the net rotation matrix for this sequence of rotations. Save your answer in a variable named final_rotation_matrix. Please also save any intermediate rotation matrices using the following naming sequence first_rotation_matrix for the first rotation and second_rotation_matrix for the second (and final) rotation. c. Create a markdown cell below to include a handmade diagram showing each step in this rotation sequence; indicate all relevant information regarding any reference frames. In completing this answer, you are to make use of the sympy functions for ReferenceFrame, symbols, and Matrix. You will create symbols for x, y, d, and 0. Use variable names x, z, phi, and theta. Also make use of Reference Frame to create all frames.
Consider a reference frame N comprising a set of unit vectors nx, ny, and nz. A vector v has the form: V = xnx + znz, where x and z are scalar constants. a. Express this vector in a new reference frame E, which is obtained by a positive rotation about the ny. Store your answer in a variable named v_final. b. Consider now the effect of a second rotation, 0, about the x-direction of the frame E, which results in a new frame F. What is the net rotation matrix for this sequence of rotations. Save your answer in a variable named final_rotation_matrix. Please also save any intermediate rotation matrices using the following naming sequence first_rotation_matrix for the first rotation and second_rotation_matrix for the second (and final) rotation. c. Create a markdown cell below to include a handmade diagram showing each step in this rotation sequence; indicate all relevant information regarding any reference frames. In completing this answer, you are to make use of the sympy functions for ReferenceFrame, symbols, and Matrix. You will create symbols for x, y, d, and 0. Use variable names x, z, phi, and theta. Also make use of Reference Frame to create all frames.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Solve the following problem in Python
Transcribed Image Text:Consider a reference frame N comprising a set of unit vectors nx, ny, and nz. A vector ▾ has the form: V = xnx + znz, where x and z. are scalar constants.
a. Express this vector in a new reference frame E, which is obtained by a positive rotation about the ny. Store your answer in a variable named v_final.
b. Consider now the effect of a second rotation, 0, about the x-direction of the frame E, which results in a new frame F. What is the net rotation matrix for this sequence of rotations. Save
your answer in a variable named final_rotation_matrix. Please also save any intermediate rotation matrices using the following naming sequence first_rotation_matrix for the
first rotation and second_rotation_matrix for the second (and final) rotation.
c. Create a markdown cell below to include a handmade diagram showing each step in this rotation sequence; indicate all relevant information regarding any reference frames.
In completing this answer, you are to make use of the sympy functions for ReferenceFrame, symbols, and Matrix. You will create symbols for x, y, p, and 0. Use variable names x,
z, phi, and theta. Also make use of Reference Frame to create all frames.
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