Syllabus · Fall 2014

Prof. Kate Jones-Smith

Lecture: 1-2:15 pm MWF, G041Email: kjonessm@hamilton.edu |
Office Hours: 2-4pm TR, G051 or 1038Appointments outside this time are welcome |

**Text**: Marion & Thornton, *Classical Dynamics of Particles and Systems*, 5th edition

**Description**: In classical mechanics we are concerned with the behavior of systems that can be treated in the Newtonian regime, for which electromagnetic and mi- croscopic interactions can generally be ignored. The primary means by which we study systems is by determining their ‘equations of motion’, which can be obtained using Newton’s Laws and conservation principles, or with the more sophisticated Lagrangian/Hamiltonian formalism. This approach to mechanics does not subsume Newton’s laws but replaces them; it is more elegant and has much broader scope, and it is the way we analyze systems (not just classical) in the modern era. In this course we will study both approaches. The topics we will cover are: dynamics of single par- ticles and systems of particles, the variational principle and Lagrangian/Hamiltonian mechanics, celestial mechanics and central-force motion, motion in non-inertial refer- ence frames, and oscillations including non-linear dynamics and chaos. This course is a key component of an undergraduate preparation in physics as techniques from classical mechanics form the basis for analysis in other branches of physics.

**Itinerary**: The course will be divided into three units. In the first unit we will re-visit topics and concepts you are familiar with from freshman physics; Newton’s Laws and conservation theorems for a single particle are covered in Chapter 2, then we ex- tend these principles to systems of particles in Chapter 9. We wrap up the first unit with gravitation in Chapter 5. The second unit consists of Chapters 6-8, 10 and 11. The variational principle and the Lagrangian/Hamiltonian formalism are presented in Chs. 6 and 7. We will put some of that formalism to use in Chapters 8,10, and 11, where we will study central force motion, motion in non-inertial reference frames, and dynamics of rigid bodies respectively. Finally, for the third unit we study oscillations; in Chapters 3 and 12 we study single and coupled oscillations respectively, and we conclude with non-linear dynamics and chaos from Chapter 4.

**Coursework**: The coursework will consist of three different components. There will be problem sets due roughly every week. These make up 30% of your grade in the course. There will be 3 midterm exams and one take-home final, each worth 15% of your grade in the course. There will also be presentation of homework problems (described below), which makes up 10 % of the total grade.

The problem sets will consist of approximately 6 problems, two of which will tend to be more difficult and will be presented in a rotating assignment. The idea is like a potluck, where you bring a dish to share, and in exchange you get to partake in all the dishes that other people brought. When it is your turn to present you will be responsible for obtaining the correct solution to a homework problem. You must understand the solution sufficiently well that you can clearly explain it at the board (preferably without notes) and answer your classmates’ questions. The people in the class who are not presenting get the solution to two homework problems ’for free’. On all homework assignments you are allowed to use any resource in obtaining the solution so long as you cite it during your presentation and/or on your assignment. Especially, you are welcome and encouraged to meet with me before it is your turn to present at the potluck, to discuss a solution you have obtained or if you are stuck.

On weeks that there is an exam we will not have potluck problems, or I will present them. Each person will present one potluck problem and when we are through with the entire class, depending on how much time is left, we will either start over with the roster or we will switch to toys. This will be determined at a later date.

**Etiquitte**: Physics can be a challenging subject for many. You are asked to maintain a respectful attitude in lecture. Laptops, cell phones, tablets, etc. are not allowed in lecture. If you wish to take notes it should be on paper by hand. If this poses any difficulty for you please let me know and we can find a solution that suits your needs.

**Accomodations**: I request that anyone needing academic adjustments or accom- modations speak with me during the first two weeks of class. All discussions will remain confidential. Students with disabilities should also contact Allen Harrison, Associate Dean of Students for Multicultural Affairs and Accessibility Services in the Office of the Dean of Students (Elihu Root House; ext. 4021) who coordinates services for students with disabilities.

**Important Dates**:

Unit 1: Review of Newton’s Laws & Gravity (Ch 2, 9, and 5)

Exam 1: Wednesday Oct. 1

Unit 2: Calculus of variations and the Lagrangian approach to mechanics, central force motion, non-inertial reference frames, rigid body motion (Ch 6-8,10, and 11) Exam 2: Friday Nov. 14

Unit 3: Oscillations, Non-linear dynamics and chaos (Ch 3, 4, and 12)

Exam 3: Friday Dec. 12

Final exam: Due Dec. 19 at 4pm