This course is a continuation of the treatment of mechanics
started in PH 2201. Topics covered include: rigidbody dynamics,
rotating coordinate systems, driven harmonic oscillator and normal
modes, and the Lagrangian and Hamiltonian formulations of mechanics.
Recommended background: PH
1110/11,
PH 1120/21, PH 1130, PH 1140, PH 2201,
MA 1021, MA 1022, MA 1023, MA 1024, MA
2051 and concurrent registration in or completion
of MA 2071. (The more important
courses are in bold.) In contrast to PH 2201, this
material is more theoretically oriented and much of it will be
new to you. It requires a higher level of mathematical background.
The text is "Classical Mechanics", by J.R. Taylor,
available in the bookstore. The physics library, OH 118, has a copy on
reserve. A good supplementary text, with a
lot of solved problems, is "Introduction to Classical Mechanics" by D.
Morin. We meet in OH 223 on MTWThF at 2:00
pm. Instructor:
Professor
NA Burnham,
nab@wpi.edu.
% 
Activity 
50% 
The twelve homework assignments.
No
late work
accepted. [200 pts] 
50% 
The two exams. 10%
penalty for makeups. [200 pts] 
Points  For each problem (out of five possible points): 
5  No symbolic solutions 
5 
Symbolic solution has wrong dimensions 
1 to 5  Writeup hard to read or understand 
1 
No commentary 
1  Vectors confused with scalars or vice versa 
1 
Missing or incorrect units on
numerical answers 
1  No boxes around symbolic and numerical answers 
In general, for any given problem:  
5 =  Very good  writeup clear and correct 
4 =  Good  writeup clear and mostly correct, or understandable
and correct 
3 =  Acceptable  writeup understandable and mostly correct, or
poor writeup and correct, or clear writeup and incorrect 
For
the summaries (out of five
possible points): 

5 
Equations in summary 
5 
Handwritten 
1 to 5 
Symbols in summary 
1 to 5  Not enough detail 
1 
Shorter or longer than specified length, in
increments of 50 words 
1 
No word count 
And for an entire assignment:  
5  Electronic submission 
1  No name 
1  Ragged edges 
1  No staple 
Mechanics is the study of motion. Its history dates from Galileo and Newton and was developed further by Lagrange and Hamilton. About a hundred years ago, scientists started to develop relativistic mechanics and quantum mechanics, and to distinguish among them, the traditional form of mechanics has become known as "Classical Mechanics."
Newton's famed three laws of motion are based upon ideas that concern space, time, mass, and force. Space can be described by coordinate systems, the simplest one being the cartesian coordinate system, which has three orthogonal axes. The position of an object can be determined by a position vector, and the next few pages of the text reviews vector algebra. After further reminders of time, reference frames, mass, and force, Newton's laws are introduced.
The First Law says that a particle moves with a constant velocity unless acted upon by an external force. The Second Law states the relationship between mass, a scalar, and acceleration, a vector. Their product equals the vector sum of all the forces acting on a particle. Since acceleration is the second derivative of position with respect to time, the Second Law is a differential equation. Newton's Laws hold in what are called inertial reference frames. They do not always hold for relativistic or quantum systems. Nonetheless, they are valid over a wide range of scales in size and speed and are thus worthy of study.
The Third Law states the relationship between "action" forces and "reaction" forces. They are equal in magnitude and opposite in direction, but act on two different bodies. From the Third Law, which considers only one particle, one can construct a theory for many particles. Internal forces in a multiparticle system have no influence on the total momentum. In other words, if the external forces are constant, then momentum is conserved. Taylor gives an example where, apparently, the Third Law is violated, but then explains that mechanical momentum is not the only form of momentum. It can, for example, be electromagnetic. However, Taylor assures us that for the rest of his text, we will consider situations only in which the Third Law holds.
353 words
Supplementary proglems 
Homework problems 
Supplementary problems  Homework problems 
 
 
SP0:
P.6.1 
HW0:
Solve Problem 6.2;
summarize
Sections 6.06.3. The calculus of variations is our leadin
to Lagrangian mechanics. [10 pts] 
SP1: P.7.1, 7.15.  HW1: Solve Problems 7.3, 7.18; summarize Sections 7.07.4. After you learn to use Lagrangians well, you will wonder why you were taught anything else. [15 pts]  SP2:
P.7.31,
7.37. 
HW2: Solve Problems 7.27, 7.40; summarize Sections 7.57.8. Section 7.8 is our introduction to the Hamiltonian. [15 pts] 
SP3: P.13.1, 13.13.  HW3: Solve Problems 13.6, 13.23; summarize Sections 13.013.6. The Hamiltonian is commonly used in quantum mechanics, a subject that many of you will study next year. [15 pts]  SP4:
P.9.2, 9.3. 
HW4: Solve Problems NAB1, NAB2; summarize Sections 9.09.5. The topic is noninertial frames, notably the Earth and the origin of the tides, and centrifugal force. [15 pts] 
SP5:
P.9.8, 9.15. 
HW5: Solve Problems NAB3, NAB4. Summarize Sections 9.69.10. More on noninertial frames, including the Coriolis force and its affect on the motion of projectiles. [15 pts]  SP6:
P.9.16, 9.27. 
HW6: Solve Problems 9.18, 9.30; summarize Sections 10.010.3. How the distribution of mass within a rotating body affects its motion. [15 pts] 
SP7: P.10.4, 10.11, 10.23.  HW7:
Solve Problems NAB5, NAB6, 10.18; summarize Sections
10.410.8. The precession of tops. [20 pts] 
SP8: P.10.29, 10.35, 10.40. NOT 10.43.  HW8: Solve Problems 10.30, 10.36, 10.47; summarize Sections 11.011.4. Many reallife systems can be modeled as a set of interacting springs. [20 pts] 
SP9: P.11.1, 11.5.  HW9: Solve Problems NAB7, NAB8, NAB9; summarize Sections 11.511.7. The coordinated movements of interacting springs and masses. [20 pts]  SP10: P.11.15, 11.20, 11.24, 11.32.  HW10: Solve Problems NAB10, NAB11, NAB12. Summarize Sections 12.012.4. The characteristics of and approach to chaos. [20 pts] 
SP11: P.12.12,
12.13, NOT 12.27 
HW11: Solve Problems 12.11, 12.16, 12.19; summarize Sections 12.512.8. Methods of describing chaos. [20 pts]  

 
Week of  Monday  Tuesday  Wednesday  Thursday  Friday 
25.
October 2009 
What's
due Today's material Sections 
 Introduction 6.06.3 
 Unconstrained motion 7.07.1 
SP0 Constraints 7.27.4 
HW0e Examples 7.5 
1. November  SP1 Conservation laws 7.67.8 
HW1e Hamilton 1D 13.013.2 
 Hamilton nD 13.313.6 
SP2 Tides 9.09.2 
HW2 Rotating frames 9.39.5 
8. November  SP3 NO CLASS THIS WEEK 
HW3 Submit to Nick Hoar nikx@wpi.edu 
   
SP4   
HW4 Submit to Nick Hoar nikx@wpi.edu 
15. November  SP5 Centrifugal force 9.6 
HW5 Coriolis force 9.79.8 
 Foucault 9.99.10 
SP6 Examples Chap. 9 
HW6 CM, I 10.010.2 
22. November   Review Chaps. 6,7,13,9 
 EXAM 1 Chaps. 6,7,13,9 
Suggestion: Do the rest of the reading summaries over Thanksgiving. 

29. November  SP7 Inertia tensor 10.3 
HW7 Principal axes 10.410.5 
 Precession 10.610.8 
SP8 Examples Chap. 10 
HW8h Normal modes 11.011.3 
6. December 
SP9 Helpful Lagrangians 11.4 
HW9h The general case 11.511.7 
 Examples Chap. 11 
SP10 Approach to chaos 12.012.5 
HW10h Chaos 12.612.8 
13. December 
SP11 Review Chap. 10 
HW11 Review Chaps. 1112 
 EXAM 2 Chaps. 1012 
Fun? 
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