# PHYS 381  SYLLABUSFall 2013

CATALOG DESCRIPTION:  PHYS 381   Advanced Mechanics II

A continuation of the study of mechanics including accelerated reference frames, generalized coordinates and Lagrangian and Hamiltonian mechanics.

Prerequisite:  PHYS 380 and MATH 232.                  One semester; three credits

TEXT:   Mechanics   by Symon is recommended but not required; study guides and notes including homework problems are provided on the course web page

INSTRUCTOR:  Dr. Johnny B. Holmes, Professor of Physics
office:  CW 103                     office phone:  321-3448                   e-mail:  jholmes@cbu.edu

### PREREQUISITES BY TOPICS:

Newton’s laws of motion, conservation of energy, conservation of linear momentum, conservation of angular momentum, differential equations, and vector calculus.

GOALS:

1.  To train the student to think about physical phenomena in mathematical terms.

2.  To deepen the student’s understanding of the basic laws of Newtonian (classical) mechanics

a)  using calculus and differential equations;

b)  using different coordinates.

3.  To become familiar with order of magnitude estimates of various physical parameters and

phenomena.

4.  To increase the student’s ability to apply scientific principles and methods by applying them to a particular area of investigation.

### TOPICS:

• Moving Coordinate Systems
• Moving Coordinate Systems - The basics
• Rotating Coordinate Systems
• Effective Gravity
• Foucault Pendulum
• Larmor's Theorym
• Restricted Three-Body Problem
• Lagrangian and Hamiltonian Functions
• Generalized Coordinates
• Generalized Momentum, Force, and the Lagrangian
• Constraints
• Ignorable Coordinates and Constants of the Motion
• Hamilton's Equations
• Electro-Magnetic Forces and a Velocity-Dependent Potential

Grading will be based on both tests and homework.  On the test part there will be two tests and a final.  Each of these three tests will count as 1/6 of the final grade.  For each regular test you may bring in one 8½”x11” sheet of paper with writing on one side.  The questions for the tests will be taken mostly from the study questions on the study guide.  For the final you may bring in two 8½”x11” sheets of paper with writing on one side each (or one sheet with writing on both sides).  The questions for the final will come mostly from the previous tests.   On the homework part there will be 8 homework problems that will be graded and will count as ½ of the final grade.  NOTE:  YOU MUST HAVE AT LEAST 65% ON YOUR HOMEWORK GRADE TO PASS THE COURSE.  Assuming you do have at least a 65% on your homework grade, your final grade will be based on the following scale:

A: 90‑100;  B: 80‑90;  C: 65‑80;  D: 60‑65;  F: 0‑60

The homework will be assigned with a due date of the test date for the section which it covers.  Homework that is not turned in before the test on the due date will incur a 20% penalty, and homework that has not been turned in two weeks from the due date will incur a 30% penalty.  Homework will not be accepted for credit after the last day of regular classes for the semester.  Each homework problem will normally be worth 10 points.  Your homework grade will be your total homework score divided by 80, and this fraction will be multiplied by 100 for your homework score (which is half of your course grade).

Homework should be legible and easily followable.  Any equations used should be identified with words, and intermediate mathematical steps should be included.  Answers should be shown to be reasonable by arguments based on examination of limiting cases and common sense whenever possible.  Homework will normally be returned at the next class and may be redone and re‑submitted based on the comments or corrections, but the re‑submitted homework will be subject to the same grading time‑frames as the original specified above unless otherwise specified at the time.  For example, if you turn in a homework assignment on the due date, and it is returned the next class with a 5/10 grade, you may resubmit a corrected version the next week for a maximum of 8/10.  If the redo is submitted before the due date, you may still earn up to full credit on that assignment.

ABSENCES:

Class absences will not be counted, but homework due dates will be maintained regardless of class attendance.  Test absences will incur a 10% penalty with a good excuse or a 20% penalty without a good excuse, and a make‑up test will be given as soon as can be arranged.  If you know beforehand that you will miss a test, you can contact me and arrange to take it early with no penalty ‑ but I need at least 24 hours notice to have the test ready.

Tentative schedule for topics:

Class #1:  Coordinate Systems – a Review  +  Moving Coordinate Systems

Class #2:  Rotating Coordinate Systems

Class #3:  Rotating Coordinate Systems (cont.)  +  Effective Gravity

Class #4:  Foucault Pendulum  +  Larmor’s Theorem

Class #5:  Restricted 3-body Problem

Class #6:  Test #1

Class #7:  Generalized Coordinates

Class #8:  The Lagrangian

Class #9:  The Lagrangian (cont.)

Class #10: Constraints

Class #11:  Ignorable Coordinates

Class #12:  Hamilton’s Equations

Class #13:  Electric and Magnetic Forces

Class #14:  Test #2

NOTE:  At present, the class is listed as TBA.  We can either meet once a week for the whole semester, or we can meet twice a week starting at the beginning of the semester and ending at fall break (midterm).  Homework can be worked on during the whole semester regardless of which class schedule we end up with.