YourName-HW05

your name
the date you completed the first version;  date of most recent revision
This template was revised March 3, 2021.

Introduction and Statement of Problem

The purpose of this notebook is to gain some experience finding the distance and azimuth between two points on a spherical Earth.

Statement of Problem.  A vector a is defined as a = {1,2,0} and extends to a point A in the XYZ coordinate system.  
(a) What are the coordinates of the vector to point A (call it vector a’) in a X’Y’Z’ coordinate system in which the Z and Z’ axes coincide with one another and the X’ axis is rotated 47° anti-clockwise from X (and so Y’ is 47° from Y).  An anti-clockwise rotation is considered a positive rotation.
(b) What are the coordinates of that vector to point A (call it vector a”) in a X”Y”Z” coordinate system in which the Z and Z” axes coincide with one another and the X” axis is rotated 63° clockwise from X (and so Y” is 63° from Y).  A clockwise rotation is considered a negative rotation.
     Write a Mathematica notebook that analyzes the input data to answer questions (a) and (b).

Input Data

(a)  theta = 47°, vectorA={1,2,0}

(b)  theta = -63°, vectorA={1,2,0}

Computation

Part A

Define the vector to point A in the XYZ coordinate system

vectorA=(({{1}, {2}, {0}}));

Define the angle theta

thetaA=47;

Define the transformation matrix J

matrixJA=(({{Cos[thetaA Degree], Sin[thetaA Degree], 0}, {-Sin[thetaA Degree], Cos[thetaA Degree], 0}, {0, 0, 1}}));

Define the vector to point A in the X’Y’Z’ coordinate system

In the space immediately following this line, create an input line to define vectorAPrime and suppress the output with a semicolon at the end of the input line.

Part B

Define the vector to point A in the XYZ coordinate system

vectorA=(({{1}, {2}, {0}}));

Define the angle theta

thetaB=-63;

Define the transformation matrix J

matrixJB=(({{Cos[thetaB Degree], Sin[thetaB Degree], 0}, {-Sin[thetaB Degree], Cos[thetaB Degree], 0}, {0, 0, 1}}));

Define the vector to point A in the X”Y”Z” coordinate system

In the space immediately following this line, create an input line to define vectorADoublePrime and suppress the output with a semicolon at the end of the input line.

Output Data

Answer to Part A

In the space immediately following this line, create an input line to output the numerical result of the vector transformation in Part A, in matrix form.

Answer to Part B

In the space immediately following this line, create an input line to output the numerical result of the vector transformation in Part B, in matrix form.

References

Cronin, V.S., 2021, Kinematics-Chapter-3.nb:  unpublished draft, http://croninprojects.org/Vince/PlateKinematics/KinematicsCourse/Kinematics-Chapter-3.nb.pdf

Cronin, V.S., 2017, A brief primer on plate kinematics, with Mathematica:  unpublished draft, http://croninprojects.org/Vince/PlateKinematics/KinematicsPrimer/KinematicsCh3.nb