| croninprojects.org/ Vince/ PlateKinematics/ KinematicsCourse/Mathematica-Assignments.html |
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This course is taught by Professor Vince Cronin
Hints about how to code a given assignment are provided in the draft text available via http://croninprojects.org/Vince/PlateKinematics/KinematicsPrimer/index.htm . From within a Mathematica notebook, additional coding help and tutorials can be accessed by going to the "Help" menu.
A template for Mathematica homework notebooks is available at http://croninprojects.org/Vince/PlateKinematics/KinematicsCourse/LastName-HWxx.nb
| HW # | Date Assigned | Date Due | Assignment |
|---|---|---|---|
| 1 | January 19 | January 24 | Exercise 2.1 Use Google Earth to find the latitude and longitude of some place that is of interest to you, using decimal degrees. Create a Mathematica notebook with headers for its title, introduction, input data, computation, output, and references (if any). Save the notebook using your last name as the first part of the notebook name, then the homework number. For example, "Cronin-HW01". Add text to the notebook providing your name, the date you began and completed the notebook, a statement of the problem, and relevant explanations of the variables and code. Finally, add input lines of executable code. The purpose of this notebook is to compute the unit location vector to the point that is of interest to you. Cronin's standard notebook for this homework is available here as an example of what you should hand-in for coding assignments. |
| 2 | January 26 | January 31 | Exercise 2.2 You are given a vector a with components {4, 2, 7} and a vector b = {-2, 5, -4}. Write a Mathematica notebook that analyzes the input data to complete the following tasks. (a) Compute the vector cross product a x b (a cross b) to yield the vector c, and list the components of vector c (b) Determine the length of vector c (c) Determine the angle between vectors a and c (d) Determine the angle between vectors b and c (e) What can you say about the orientation of vector c relative to vectors a and b that will be generally true given any such non-zero, non-colinear vectors a and b? |
| 3 | January 31 | February 7 | Exercise 2.3 In the early Miocene ~23 million years ago, a volcano erupted in California. Sometime later in the Miocene, the San Andreas fault propagated through the volcanic field, and separated it into what is now the Pinnacles National Monument (36°29'13"N, 121°10'01"W) on the west side of the fault and the Neenach volcanic field (34°44'24"N, 118°37'24"W) on the east side (Matthews, 1973). Write a Mathematica notebook that analyzes the input data to complete the following tasks. (a) Convert the geographic coordinates to unit location vectors, recalling that south latitudes and west longitudes are negative numbers. (b) Determine the angular distance between the Pinnacles and Neenach. (c) Find the circumferential distance between the Pinnacles and Neenach, assuming that Earth is a sphere of radius 6,371.01 km. (d) Find the azimuth of Pinnacles as viewed from Neenach, and of Neenach as viewed from Pinnacles. (e) What geological statement can you make about displacement along the San Andreas fault? |
| 4 | February 7 | February 9 | Exercise 3.1 Write a Mathematica notebook that solves 2-D problems of the sort described in Exercises 3.1a and 3.1b that works with any vector when the angle between the two coordinate systems is a positive number and also works when that angle is a negative number. (a) You are given a vector a with components {2, 3} in an X-Y coordinate system. Write a Mathematica notebook that determines the components of that vector in an X'-Y' coordinate system that is oriented 20° (i.e., in a positive or counter-clockwise direction) from the X-Y system, shares a common origin, and is in the X-Y plane. (b) You are given a vector b with components {4, 7} in an X-Y coordinate system. Write a Mathematica notebook that determines the components of that vector in an X'-Y' coordinate system that is oriented -50° (i.e., clockwise) from the X-Y system, shares a common origin, and is in the X-Y plane. |
| 5 | February 9 | February 14 | Exercise 4.1 Write a Mathematica notebook that computes the location vector for a point initially located at latitude 16° north and longitude 38° east, as well as the location vector after that point has rotated anticlockwise (toward the east) around the north pole by 165°. |
| 6 | February 9 | February 14 | Exercise 4.2 Write a Mathematica notebook that computes the location vector p0 for a point P initially located at latitude θ = 16° and longitude φ = 38°, as well as the location vector p1 after that point has rotated anticlockwise (toward the east) around the north pole for t = 3.5 hours at a rate of ω = 15°/hour. Finally, evaluate the notebook and output the answers. |
| 7 | February 14 | February 16 | Exercise 4.3 Write a Mathematica notebook that creates a table of distances for a 1963 Volkswagen Beetle traveling in a straight line at a constant speed of 100 km/hour for four hours in 10-minute steps. The first value in the table should be zero. |
| 8 | February 14 | February 17 | Exercise 4.4 Write a Mathematica notebook that computes the location of a point initially located at latitude 72°N, longitude 15°W every hour for a day, and saves it in a table. Be economical -- use the fewest lines of code you can, but add explanatory text as needed. |
| 9 | February 14 | February 17 | Exercise 4.5 Add to the code you wrote in Exercise 4.4, so that it plots the location data you computed on a sphere using the module spherePlot1. |
| 10 | March 3 | March 16 | Exercise 6.5-1 The little bridge along the Parkfield-Coalinga road near Parkfield, California, is one of the most famous bridges in the world, at least to seismologists. Seismologists who get out of their offices and look at actual faults, that is. The bridge has been rebuilt many times, in large part because the San Andreas fault passes between the northeast and southwest ends of the bridge. According to Google Earth, the bridge is located at 35.895172°N latitude and 120.434657°W longitude. The current best estimate for the location of the instantaneous pole of motion around which the Pacific plate rotates relative to North America is 48.9°S latitude and 108.3°E longitude, with an angular velocity of 0.750°/Myr (DeMets and others, 2010). Write a Mathematica notebook that computes the direction (azimuth) and magnitude (cm/yr) of the instantaneous tangential motion of the Pacific plate relative to the North American plate at the Parkfield bridge. |
| 11 | March 3 | March 16 | Exercise 6.5-2 UNAVCO maintains web-accessible datasets from geodetic GPS stations throughout the United States and elsewhere. One of the GPS stations is called CARH (short for CARH_SCGN_CN2001), and is located at 35.88839°N latitude and 120.43082°W longitude, near the Parkfield bridge on the Pacific side of the San Andreas fault. The motion of CARH relative to the North American reference frame (NAM08) is expressed as north-south, east-west, and up-down velocity vectors on the time-series graphs that are accessible at http://www.unavco.org/instrumentation/networks/status/pbo/overview/CARH. The CARH data were accessed on March 2, 2017, and the NAM08 velocities were 26.51±0.19 mm/yr toward north, 20.21±0.17 mm/yr toward west, and 1.02±0.24 mm/yr up. [A] Using only the horizontal velocities, determine the direction (azimuth) and magnitude (cm/yr) of the motion of CARH relative to the stable cratonic interior of North America. (You can do this with a calculator, the Pythagorean Theorem, and the SOH CAH TOA mnemonic to help solve right-triangle problems.) How does the GPS velocity vector compare with your answer for Exercise 6.5-1? [B] Now do the same for PBO station HOGS, located SW of CARH at 35.86672°N latitude and 120.47950°W longitude, where the horizontal velocities were 29.30±0.06 mm/yr toward north, 21.91±0.08 mm/yr toward west, and 2.80±0.40 mm/yr down (http://www.unavco.org/instrumentation/networks/status/pbo/overview/HOGS). CARH is located quite near to the San Andreas fault trace, and HOGS is 5 km from the fault on the Pacific side. [C] Is there a difference in tangential (horizontal) velocities at the two PBO sites, and if so, form a hypothesis to account for this difference. How might you test your hypothesis? |
Revised March 9, 2017
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