YourName-HW06

your name
the date you completed the first version;  date of most recent revision
This template was revised March 7, 2021.

Introduction and Statement of Problem

The purpose of this notebook is to find the location of four points after a positive and a negative rotation of a model Earth around its spin axis.

Statement of Problem.  Consider four points (A, B, C, and D) on the globe whose initial locations in the room CS and globe CS are as follows: (Subscript[latitude, A]) = 16°, (Subscript[longitude, A]) =38°;  (Subscript[latitude, B]) = 34°, (Subscript[longitude, B]) =-26°;  (Subscript[latitude, C]) = -44°, (Subscript[longitude, C]) =-37°;  and  (Subscript[latitude, D]) = -19°, (Subscript[longitude, D]) =43°. 
Using the template provided, complete a Mathematica notebook that computes the location vectors for this set of points in the room CS (a) after a rotation of 47° around the North Pole from the initial position, and (b) after a rotation of -56° around the North Pole from the initial position.

Input Data

Define the geographic coordinates of the four points:  A, B, C, and D

Variable latitudeA is defined as 16 (where the implied unit is degrees), and variable longitudeA is defined as 38.  This one is done for you as an example.

latitudeA=16;
longitudeA=38;

Variable latitudeB is defined as 34, and variable longitudeB is defined as -26

Variable latitudeC is defined as -44, and variable longitudeC is defined as -37

Variable latitudeD is defined as -19, and variable longitudeD is defined as 43

Define the two theta angles (theta1 for part (a) and theta2 for part (b))

Variable theta1 is defined as 47 degrees and is used to solve part (a) of this problem

Variable theta2 is defined as -56 degrees and is used to solve part (b) of this problem

User-Defined Function

The user-defined function makeLocationVector acts on input geographic coordinates (decimal latitude and decimal longitude, both expressed in degrees) and returns the Cartesian-geographic coordinates of the unit location vector to that point.  This user-defined function is copied from the document “Kinematics-Chapter-2.nb.pdf” by Vince Cronin.

makeLocationVector[lat_, long_]:={Cos[lat Degree] Cos[long Degree], Cos[lat Degree] Sin[long Degree], Sin[lat Degree]};

Computation

Define the unit location vectors in the Cartesian geographic coordinate system

Variable vectorA is the unit location vector to point A at the beginning of the experiment, computed using makeLocationVector[].  This one is done for you as an example.

vectorA=makeLocationVector[latitudeA,longitudeA];

Variable vectorB is the unit location vector to point B at the beginning of the experiment, computed using makeLocationVector[]

Variable vectorC is the unit location vector to point C at the beginning of the experiment, computed using makeLocationVector[]

Variable vectorD is the unit location vector to point D at the beginning of the experiment, computed using makeLocationVector[]

Define the transformation matrix (Subscript[J, 1]) used to solve part (a) of this problem

matrixJ1=(({{Cos[theta1 Degree], -Sin[theta1 Degree], 0}, {Sin[theta1 Degree], Cos[theta1 Degree], 0}, {0, 0, 1}}));

Define the transformation matrix (Subscript[J, 2]) used to solve part (b) of this problem

matrixJ2=(({{Cos[theta2 Degree], -Sin[theta2 Degree], 0}, {Sin[theta2 Degree], Cos[theta2 Degree], 0}, {0, 0, 1}}));

Find the unit location vector to each of the four points in the “room” CS after they have been rotated by theta1 degrees

Variable vectorArotated1 is the location vector to point A, in the room CS, after the globe has been rotated by theta1 degrees.  Suppress the output by ending your input line with a semicolon.  This one is done for you as an example.

vectorArotated1=Dot[matrixJ1,vectorA];

Variable vectorBrotated1 is the location vector to point B, in the room CS, after the globe has been rotated by theta1 degrees.  Suppress the output by ending your input line with a semicolon.

Variable vectorCrotated1 is the location vector to point C, in the room CS, after the globe has been rotated by theta1 degrees.  Suppress the output by ending your input line with a semicolon.

Variable vectorDrotated1 is the location vector to point D, in the room CS, after the globe has been rotated by theta1 degrees.  Suppress the output by ending your input line with a semicolon.

Find the unit location vector to each of the four points in the “room” CS after they have been rotated by theta2 degrees

Variable vectorArotated2 is the location vector to point A, in the room CS, after the globe has been rotated by theta2 degrees.  Suppress the output by ending your input line with a semicolon.

Variable vectorBrotated2 is the location vector to point B, in the room CS, after the globe has been rotated by theta2 degrees.  Suppress the output by ending your input line with a semicolon.

Variable vectorCrotated2 is the location vector to point C, in the room CS, after the globe has been rotated by theta2 degrees.  Suppress the output by ending your input line with a semicolon.

Variable vectorDrotated2 is the location vector to point D, in the room CS, after the globe has been rotated by theta2 degrees.  Suppress the output by ending your input line with a semicolon.

Output Data

Answers to part (a)

In the space immediately following this line, create input lines to show the numerical results of the rotation in part (a), in matrix form.  One is provided for you as an example.

MatrixForm[N[vectorArotated1]]

Answers to part (b)

In the space immediately following this line, create input lines to show the numerical result of the rotation 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