YourName-HW07

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 a point A whose current location in the Earth CS and Earth-Sun CS is as follows: (Subscript[latitude, A]) = 16°, (Subscript[longitude, A])=38°.  Given Earth’s angular velocity of 15°/hr around the North Pole, complete a Mathematica notebook that computes the location vector for point A in the Earth-Sun CS (a) five hours in the future, and (b) three hours in the past.

Input Data

Define the geographic coordinates of point A

Variable latitudeA is defined as 16 (where the implied unit is degrees), and variable longitudeA is defined as 38.

Define the angular speed omega

Variable omega is defined as 15, and the units are “degrees per hour.”

Define the time variable for part (a) and part (b)

Variable timeA is defined as 5, and variable timeB is defined as -3.

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 vector 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[].

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

matrixJ1=(({{Cos[(omega*timeA) Degree], -Sin[(omega*timeA) Degree], 0}, {Sin[(omega*timeA) Degree], Cos[(omega*timeA) Degree], 0}, {0, 0, 1}}))

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

matrixJ2=(({{Cos[(omega*timeB) Degree], -Sin[(omega*timeB) Degree], 0}, {Sin[(omega*timeB) Degree], Cos[(omega*timeB) Degree], 0}, {0, 0, 1}}))

Find the unit location vector to point A in the “room” CS after it has been rotated by (omega×timeA) degrees

Variable vectorArotated1 is the location vector to point A, in the room CS, after the globe has been rotated by (omega*timeA) 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];

Find the unit location vector to point A in the “room” CS after it has been rotated by (omega×timeB) degrees

Variable vectorArotated2 is the location vector to point A, in the room CS, after the globe has been rotated by (omega*timeB) 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