PHYS 522 Mechanics

Current semester class files are listed here.  Past semester files are listed here.  Schedule can be found below.

PHYS522 – Mechanics – Spring 2009

Textbook:   Classical Mechanics, John R. Taylor
 

Suggested References: Analytic Mechanics, Fowles; Classical Mechanics, Goldstein; Wave Physics, Nettel; Mathematical Methods for Physicists, Arfken and Weber; Classical Dynamics of Particles and Systems, Fifth Edition, Thorton and Marion

Instructor: Dr. Brian R. Washburn CW 36B, (785) 532-2263  Office hours: M/W/F 9:30-10:30 PM or by appt.

Purpose and Goals:  The purpose of this course is to expose you to advanced formalisms of classical mechanics, thus introducing the foundation for other areas of physics.  Another important purpose is to for you to develop a strong conceptual understanding of mechanics, and to develop the problem-solving techniques needed to handle sophisticated problems in classical mechanics.

The overall goals of this class are:

·    Introducing “new” formalisms of classical mechanics and how these formalisms are related to other areas of physics.

·    Expanding your current knowledge of mechanics.

·    Introducing the concept of symmetry and its relationship to conservation principles.

·    Developing essential mathematical and numerical methods and tools.

·    Improving your writing and problem-solving skills

·    Improving your conceptual understanding of mechanics, and your ability to communicate your knowledge.

Grading:  

Exam 1

100 pts

200 pts

Exam 2

100 pts

Final Exam

300 pts

Homework

480 pts

Quizzes

20

Total possible

1000 pts

 

Exams:  There will be two exams plus a cumulative final exam.  The exams will either be in-class or a take home exam, to be agreed upon by the class and instructor. 

In-Class Quizzes:  Surprise quizzes on the reading material may be given during the lecture or recitation.  The purpose of the quiz is the make you read the book before attending class.

Homework:  It is expected that you will learn the course material mostly by completing the homework.  Note that the course material will be challenging, so you will need to work hard on the homework to be successful.  Homework assignments will be given approximately once per week and will take about 10 hours.  Discussing the homework with your classmates is encouraged but you should be able to write up the assignment on your own.  In the case when you get stuck on a problem, credit will be given for a statement indicating how your solution is incorrect.

Guidelines for the homework:

·    Read the textbook before doing the homework

·    Draw a detailed diagram, write down the given variables, and write out what is to be found.

·    Think about the solution beforehand, and then see if the guess corresponds to your solution. 

·    Discuss the homework with your classmates but write the homework out on your own.

·    Ask thoughtful questions if you get stuck.

·    It is important for you, the scientist in-training, to learn how to communicate scientific information in a clear and precise manner.  It is your responsibility to present the homework solutions in a readable and logical manner.  If this is not done there will be a grade penalty.

Tentative Course Schedule, Mechanics PHYS 522, Spring 2008

Date

L/R

Topic

Book

Homework

Jan. 17 (Th)

L1

Course introduction, review of Newton’s laws

Ch. 1

 

Jan. 21 (M)

 

*** Student Holiday ***

 

 

Jan. 22 (Tu)

L2

Forces and torques, linear and angular momenta

Ch. 1

 

Jan. 24 (Th)

L3

Cylindrical coordinates, projectile motion with air resistance

Ch. 2

HW1 Due

Jan. 28 (M)

R1

Velocity and acceleration in different coordinate systems, HW1

 

 

Jan. 29 (Tu)

L4

Linear and quadratic air resistance

Ch. 2

 

Jan. 31 (Th)

L5

Motion of a charge in a uniform magnetic field

Ch. 2

HW2 Due

Feb. 4 (M)

R2

Introduction to differential equations, Go over HW2

 

 

Feb. 5 (Tu)

L6

Conservation of momentum, center of mass

Ch. 3

 

Feb. 7  (Th)

L7

Angular momentum of single and several particles

Ch. 3

HW3 Due

Feb. 11 (M)

R3

Numerical methods of integration, Go over HW3

 

 

Feb. 12 (Tu)

L8

Work, kinetic energy and potential energy

Ch. 4

 

Feb. 14 (Th)

L9

Conservation of energy, force as the gradient of potential energy

Ch. 4

HW4 Due

Feb. 18 (M)

R4

Numerical methods for differential equations

 

 

Feb. 19 (Tu)

L10

Simple harmonic motion, phase space pictures

Ch. 5

 

Feb. 21 (Th)

L11

Damped oscillations and resonance

Ch. 5

HW5 Due

Feb. 25 (M)

R5

The Fourier series

 

 

Feb. 26 (Tu)

L13

Driven damped oscillations

Ch. 5

 

Feb. 28 (Th)

L14

More oscillations: frequency of small oscillations

Ch. 5

HW6 Due

Mar. 3  (M)

R6

Review for Exam 1

 

 

Mar. 4 (Tu)

 

Exam 1

 

 

Mar. 6 (Th)

L15

Nonlinear oscillations and chaos

Ch. 12

 

Mar. 10 (M)

R7

Go over Exam 1

 

 

Mar. 11 (Tu)

L16

The calculus of variations

Ch. 6

 

Mar. 13 (Th)

L17

Lagrangian mechanics and Hamilton’s principle

Ch. 7

HW8 Due

 

 

*** Spring Break: March 17-21 ***

 

 

Mar. 24 (M)

R8

Coupled differential equations, HW 8

 

 

Mar. 25 (Tu)

L18

Generalized coordinates and constraints

Ch. 7

 

Mar. 27 (Th)

L19

Problems in Lagrangian mechanics: frequency of small oscillations

Ch. 7

HW9 Due

Mar. 31 (M)

R9

Go over HW9

 

 

Apr. 1 (Tu)

L20

Lagrangian multipliers and constraints

Ch. 7

 

Apr. 3 (Th)

L21

Conservation laws revisited!, Noether’s theorem

Ch. 7

HW 10 Due

Apr. 7   (M)

R10

Go over HW10

 

 

Apr. 8   (Tu)

L22

Hamiltonian dynamics, formalisms in physics

Ch. 13

 

Apr. 10 (Th)

L23

Two-body central force problems, reduced mass

Ch. 8

HW 11 Due

Apr. 14  (M)

R11

Go over HW11, plotting potentials by hand

 

 

Apr. 15 (Tu)

L24

Effective potentials, stable orbits

Ch. 8

 

Apr. 17 (Th)

L25

Kepler’s problem

Ch. 8

HW 12 Due

Apr. 21 (M)

R12

Review for Exam 2

 

 

Apr. 22 (Tu)

 

Exam 2

 

 

Apr. 24 (Th)

L26

Mechanics in noninertial reference frames

Ch. 9

 

Apr. 28 (M)

R13

Go over Exam 2

 

 

Apr. 29 (Tu)

L27

Rotational motion of rigid bodies, moment of inertia tensor

Ch 10

 

May 1 (Th)

L28

Euler’s equations, gyroscopes

Ch. 10

HW 13 Due

May 5 (M)

R14

Linear algebra: Eigenvectors and eigenvalues, HW13

 

 

May 6  (Tu)

L29

Coupled oscillators

Ch. 11

 

May 8  (Th)

L30

Coupled oscillators and normal coordinates

Ch. 11

HW 14 Due

May 15 (Th)

 

Final Exam 9:40 a.m. - 11:30 a.m.