This course covers the fundamental principles of Newtonian and Lagrangian mechanics, together with applications including conservation laws, planetary motion, oscillations, waves, systems of particles, rigid bodies, and rotation. The goal of the course is to develop mathematical, computational (with *Mathematica ®*), and physical tools to solve a wide variety of mechanics problems. The grade will be determined by homework, a course project, and two exams.

**Time and Location:** MWF, 11-12 am in 318 Willamette Hall

**Instructor:** Prof. Benjamín J. Alemán, baleman at uoregon dot edu

**Office:** 178 Willamette Hall **Phone:** 541.346.3321

**Office Hours:** Mondays and Fridays from 12-1 pm, by appointment, or whenever my office door is open

**Graduate Teaching Fellow:** Saba Moslehi, sabam at uoregon dot edu

**GTF Office Hours: **Wednesday 4-5 pm and Thursday 2-3 pm, both in Willamette 72, and in Drop-in center Wednesday from 1-2 pm.

**Text:** *Classical Mechanics* by John R. Taylor (errata here)

Other good books (on reserve in the Science Library):

Fowles & Cassiday, *Analytical Mechanics*, 7th edition (Brooks-Cole, 2005)

Marion & Thornton, *Classical Dynamics *(4^{th} ed., Brooks-Cole, 1995)

Goldstein, Poole & Safko, *Classical Mechanics *(Addison-Wesley, 2002)

**Grading:**

Grades are based on homework, a course project, the midterm, and the final exam:

**Homework: 30%**

**Project: 10%**

**Midterm: 25%**

**Final exam: 35%**

**Homework** is due once a week, starting week 2, and counts for **30%** of your grade. Assignments will be posted here on the website. Homework must be turned into the 411 box in the basement of Willamette Hall by 7 pm each Thursday, unless otherwise specified. Late homework will be marked down 25% for the first day; homework turned in more than one day late will be marked as a zero. If you have a legitimate reason for turning in homework late, please let me know ASAP. Homework should be worked on individually, not as a group. Your homework must be neat and legible; messy, illegible homework will be returned ungraded and marked as a zero. Remember, messy work is indicative of a messy mind; slow down and do it right ☺. The course GTF will be available several hours per week to assist you in your homework.

- We will be learning to use
*Mathematica*to solve some mechanics problems computationally, and you will be assigned an occasional homework problem that requires*Mathematica*. Please download and install a free copy of*Mathematica*through the University of Oregon’s site license by following the instructions here: https://it.uoregon.edu/software/mathematica. Alternatively, you can access*Mathematica*in the Science and Mathematics library computer workstations.

You will need to choose your own unique **Course Project**. Please discuss your proposed project with me before beginning; a short written proposal will be due by **Friday, February 13 ^{th}**. Ideas for projects include writing a short paper on a mechanics-related research article, performing a numerical simulation of a mechanics problem, or reading and summarizing an extra chapter from our course text, analyzing the physics of a movie, making yourself mechanics notecards,

*etc*. The project is

**10%**of your grade and is due by the time of the Final Exam (

**Tuesday March 17**)

^{th}, 10:15 am.The** Midterm** will be on **Monday, February 9^{th}, in class**. It will be closed book, closed notes (one single-sided 8.5 “ X 11 “ formula sheet allowed), and counts for

**25%**of your grade. No excuses other than medical ones will be accepted for missing/rescheduling the exam.

**Final exam** is scheduled for **Tuesday, March 17 ^{th}, 10:15 am.** It will be closed book, closed notes (two single-sided 8.5 “ X 11 “ formula sheets, or equivalent, allowed), and counts for 3

**5%**of your grade. No excuses other than medical ones will be accepted for missing/rescheduling the exam.

**Course Documents:**

Lecture Notes:

Exams and Solutions:

Selected Mathematics Topics (from Meriam, Kraige, *Engineering Mechanics: Statics*, New York: Wiley and Sons, 1997)

First Two Chapters of Taylor’s Classical Mechanics

Feyman on Forces (from Feynman, Leighton, Sands, *The Feyman Lectures on Physics: Vol I*, Massachusetts: Addison-Wesley, 1963)

Comments on Homework:

**PDFs of Mathematica Notebooks:**

Obtain a free copy of Mathematica through the University of Oregon’s site license here.

Numerical Solution to Pendulum Equation of Motion (Θ”=-SinΘ)

Numerical Solution to Linear and Quadratic Drag (solution code to extra credit on HW#2)

Driven-damped Simple Harmonic Oscillator

Fourier Series for Periodic Square Wave

**Approximate Course Schedule (will likely be altered)**

Week |
Topics and Taylor Chapters |

1 (Jan. 5-9) | Vector Algebra and Calculus; Newtonian Mechanics; Ch. 1 & 2 |

2 (Jan 12-16) | Newtonian Mechanics: examples; Momentum and Angular Momentum; Ch. 2 & 3 |

3 (Jan. 19-23) |
Energy; Ch. 4 |

4 (Jan. 26-30) | Oscillations and Fourier Analysis; Ch. 5 |

5 (Feb. 2-6) | Continuum Mechanics and Waves; Ch. 16 |

6 (Feb. 9-13) | Midterm on Monday, Feb. 9. Project Proposals due by Friday, Feb. 13th. The Calculus of Variations, Hamilton’s Principle and Lagrangian Mechanics, Hamiltonian Mechanics; Ch. 6, 7, & 13^{th} |

7 (Feb. 16-20) | The Two-Body Problem, Planetary Motion, Non-inertial reference frames; Ch. 8 & 9 |

8 (Feb. 23-27) | Rotational Motion; Rigid Bodies; Ch. 10 |

9 (March 2-6) |
Rigid Bodies; Ch. 10 |

10 (March 9-13) | Coupled Oscillators, Summary; Ch. 11 |

11 (March 16-20) Finals Week | Final Exam: 10:15 Tuesday, March 17 |

**Homework Assignments:**

Problem Set | Due Date |

#1: Taylor 1.7, 1.8, 1.12, 1.19, 1.22, 1.26, 1.31, 1.37, 1.45, 1.46, 1.48 | Thursday, January 15th by 7 p.m. |

#2: Taylor 2.7, 2.10, 2.12, 2.13, 2.20, 2.31, 2.33, 2.34, 2.43, 2.49, 2.54, Extra Credit | Thursday, January 22nd by 7 p.m. |

#3: PROBLEM #1 (DOWNLOAD) and Taylor 3.1, 3.3, 3.5, 3.11, 3.13, 3.15, 3.18, 3.21, 3.24, 3.27, 3.34, 3.35 (Extra Credit 3.37) | Thursday, January 29th by 7 p.m. |

#4: Taylor 4.21, 4.24, 4.34, 4.37, 4.39, 4.41, 4.46, 5.4, 5.29, 5.41, 5.44, 5.45 (Extra Credit 4.25) | Thursday, February 5th by 7 p.m. |

#5: Taylor 5.18, 5.31, 5.43, 5.47, 5.50, 5.56, 16.2, 16.5, Extra Credit | Thursday, February 12th by 7 p.m. |

#6: Problem #1 and Extra Credit Problem (DOWNLOAD) and Taylor 6.1, 6.16, 6.19, 6.24, 7.3, 7.8, 7.10, 7.16, 7.31, 7.41 | Thursday, February 19th b 7 p.m. |

#7: Taylor 7.20, 7.23, 7.34, 7.40, 7.46, 8.1, 8.12, 8.18 | Friday, February 27th by 7 p.m. |

#8 Taylor 9.1, 9.7, 9.8, 9.11, 9.15, 9.20, 9.31 | Friday, March 6th by 7 p.m. |

#9 Taylor 10.13, 10.14, 10.24, 10.33, 10.36 | Friday, March 13th by 7 p.m. |

This class is interesting so far!

You mean I can type anything here and it’ll become a comment?

Well, as long as it is appropriate and doesn’t violate student conduct code.

Anyway our scheduled final exam date can get changed? It is on the same day as the E&M Final for any of us who are taking both courses.

We’ll see what the rest of the class thinks about this.

I wish the department had a better approach to teach Mathematica.

It feels like we are thrown into problems expecting to have a grasp of the language already.

I have also felt this way, but I felt more strongly about it in Phys 353 when we had that one assignment with unannounced exercises that, as it turned out, you could only do in Mathematica. So far in this class, the example notebooks here on the webpage have contained pretty much all of the syntax we need to extrapolate out into other problems.

That being said, I would definitely welcome any discussion of Mathematica in lecture. Things people might want to know about include

-The way it seems NDSolve will only accept functions with names that are a single letter long

-The way it is really picky about capitalization

-Remove[“Global`*”] at the start of your code if you messed something up and it’s still storing the wrong values in your variables

-Needs[“PlotLegends`”]

-The way multiplication of variables works if you put a space in between them, but if there is no space, it thinks it’s another, longer variable that hasn’t been defined

Obviously we can’t go into a lot of detail. It may just be worth noting the huge volume of examples and discussions on the internet. Not everyone checks discussion boards, but they’re an invaluable resource. If you’re against a wall, usually, someone, somewhere on the internet has had the same problem you do, and someone else solved it in response.

yeah that would be nice. i spent a few hours working on getting the first Mathematica problem to work and just didnt have the time to attempt the second one

To be fair you don’t need to use mathematica. A lot of these problems could be done in a bunch of different ways (python, matlab, etc.)

That said, at least for me, all last year during 352-3 and last term in 412 you’ve had to do a lot of the problems by computer and do graphs and such. How had you been doing those problems without mathematica or a similar program?

Does anyone else think the prompt in question 3.4 (not assigned) is totally offensive? I mean “hobo” really? Any one could be stupid enough to jump off a train. Jeez Taylor!

I completely disagree. I do not believe the term “hobo” is offensive in any way, shape, or form. If anything it should be an empowering term!

As the great David Sedaris once said:

“Unlike someone who was evicted or lost his house in a fire, the hobo roughed it by choice. Being at liberty, unencumbered by bills and mortgages, better suited his drinking schedule, and so he found shelter wherever he could, never a bum, but something much less threatening, a figure of merriment, almost.”

Dear all,

This is Saba, TA for PHYS 411. I wanted to make a quick note about the homeworks. In solving problems please explain every step your’re doing. Also clearly state assumptions or theorems you’re using to prove or solve problems. For the problems that need to be solved by a computer software please do so, and attach a copy of your script to your homework not just the graphs. Good luck with HW 3 and have a great rest of the week.

Best,

Saba

Well, that homework got a lot more difficult pretty quickly didn’t it.