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Introductory book on continuum mechanics

by sunjin09
Tags: continuum mechanics
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sunjin09
#1
Apr6-12, 03:06 PM
P: 312
I have never had an advanced classical mechanics class, only elementary level treatments using mostly Newtonian approaches, on very simple mechanical systems. I'm interested in learning about continuum mechanics, having in mind the applications in the applied field of seismology, which studies the propagation of mechanical waves in the solid (and molten) earth. I don't need to see applications in this introductory study. My math background is mostly engineering oriented, only recently did I start some light reading on "modern math" such as abstract algebra, topology and soon, measure, Hilbert space, etc. I can do some simple vector and maybe tensor calculus, but not differential forms. I've seen some ODEs and PDEs and solutions using separation of variables, etc, but never learned any general theorems regarding the existence, uniqueness, etc. I have some experience on classical EM waves and fields and Green's functions, but mechanical waves as I understand are tensor waves, probably harder to get used to. Now where should I start to learn the basics? I don't want a book written for undergraduate engineering students with inadequate math background, in which case the treatment typically tend to become ad hoc and very awkward, but my background won't accommodate a highly rigorous treatment using lots of geometry either, is there anything in between that emphasize more on the theory rather than applications? Thank you for reading these through, if you have any suggestions it is even more appreciated.
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Jorriss
#2
Apr7-12, 01:11 PM
P: 1,066
Do you know lagrangian and hamiltonian mechanics? Your first sentence suggests not. If so, start there with Taylor (imo).
OldEngr63
#3
Apr7-12, 02:13 PM
P: 343
As fellow by the name of Morris Stern was working on such a book quite few years ago. I do not know if it was ever completed or not. Might try a search on that name. I took such a course from him many years ago.

genericusrnme
#4
Apr7-12, 02:28 PM
P: 615
Introductory book on continuum mechanics

http://www.math.odu.edu/~jhh/counter2.html
Best free textbook going, have fun

Edit;
Also, what Jorriss said, if you don't know any action based physics you should learn that first
I've had no experience with Taylor's book but I would reccomend Landau & Lifgarbagez' Mechanics book (Vol. 1 of a Course of Theoretical Physics) and Goldsteins book (I personally like the L&L book more but goldstein covers more material).
sunjin09
#5
Apr7-12, 07:21 PM
P: 312
Folks, thank you all for your input. Some of the suggestions pointed me to some very large volume of classical mechanics as part of the theoretic physics curriculum, which is not what I'm looking for. I agree reading such materials would give me a solid foundation, but that's going to take at least months of devoted study. (I'm a working professional.)

I'm mostly interested in solving the mechanical wave (acoustic and elastic) equations in continuous media, just like classical EM waves. Taylor's book has a chapter on it but it's the last one, and probably will be dependent on the previous chapters. An ideal book I'm looking for would start with some tensor analysis, followed by basic mechanical equations in media and derive some wave equations and then discussion their solutions. It should be self-contained, assuming no experience with Hamiltonian and Lagrangian mechanics. Simply speaking, I have more experience with EM waves and I wonder if there's an approach to mechanical waves similar to that. (Something similar to Griffiths EM book). Does such a book exist at all?

Please forgive me for being ignorant about this field, which I really am.
genericusrnme
#6
Apr7-12, 07:24 PM
P: 615
Quote Quote by sunjin09 View Post
Folks, thank you all for your input. Some of the suggestions pointed me to some very large volume of classical mechanics as part of the theoretic physics curriculum, which is not what I'm looking for. I agree reading such materials would give me a solid foundation, but that's going to take at least months of devoted study. (I'm a working professional.)

I'm mostly interested in solving the mechanical wave (acoustic and elastic) equations in continuous media, just like classical EM waves. Taylor's book has a chapter on it but it's the last one, and probably will be dependent on the previous chapters. An ideal book I'm looking for would start with some tensor analysis, followed by basic mechanical equations in media and derive some wave equations and then discussion their solutions. It should be self-contained, assuming no experience with Hamiltonian and Lagrangian mechanics. Simply speaking, I have more experience with EM waves and I wonder if there's an approach to mechanical waves similar to that. (Something similar to Griffiths EM book). Does such a book exist at all?

Please forgive me for being ignorant about this field, which I really am.
You're going to need that background if you want to be able to work with these things im afraid.

start with some tensor analysis, followed by basic mechanical equations in media and derive some wave equations and then discussion their solutions
The free book I posted
http://www.math.odu.edu/~jhh/counter2.html
Does this

It should be self-contained, assuming no experience with Hamiltonian and Lagrangian mechanics
The L&L book along with the Goldstein both do this, they just assume some basic understanding of the concepts of physics
sunjin09
#7
Apr7-12, 07:28 PM
P: 312
Quote Quote by genericusrnme View Post
You're going to need that background if you want to be able to work with these things im afraid.


The free book I posted
http://www.math.odu.edu/~jhh/counter2.html
Does this


The L&L book along with the Goldstein both do this, they just assume some basic understanding of the concepts of physics
But they have a whole lot of materials I'm not interested in, such as rigid body rotations, even special relativity. Are those really necessary to solve some wave equations? BTW the free book you posted looks promising, I'm going to check it out.
genericusrnme
#8
Apr7-12, 07:34 PM
P: 615
INTRODUCTION TO
TENSOR CALCULUS
AND
CONTINUUM MECHANICS
TABLE OF CONTENTS
PART 1: INTRODUCTION TO TENSOR CALCULUS
1.1 INDEX NOTATION
1.2 TENSOR CONCEPTS AND TRANSFORMATIONS
1.3 SPECIAL TENSORS
1.4 DERIVATIVE OF A TENSOR
1.5 DIFFERENTIAL GEOMETRY AND RELATIVITY
PART 2: INTRODUCTION TO CONTINUUM MECHANICS
2.1 TENSOR NOTATION FOR VECTOR QUANTITIES . . . .
2.2 DYNAMICS
2.3 BASIC EQUATIONS OF CONTINUUM MECHANICS . . .
2.4 CONTINUUM MECHANICS (SOLIDS)
2.5 CONTINUUM MECHANICS (FLUIDS)
2.6 ELECTRIC AND MAGNETIC FIELDS . . . . . . . . . .
And, you'd be surprised where they turn up.
sunjin09
#9
Apr7-12, 07:53 PM
P: 312
Quote Quote by genericusrnme View Post
And, you'd be surprised where they turn up.
OK, I realized these "irrelevant" topics are intimately connected to the stuff I want to study, but which is a better approach, Goldstein or this particular one you listed here which starts from tensors and bring in the physics as illustrations of the math?
genericusrnme
#10
Apr7-12, 08:12 PM
P: 615
I'd say go for the L&L book, get used to lagranges equations of motion (possibly hamiltons too, I can't remember if they come up in the continuum mechanics book) and the rigid body motion to get you used to working with stuff and then start on the intro to tensor calc/continuum mech
The equations of motion come up in heinbockels book and they aren't very well explained so you'll need to know about them before you start.
sunjin09
#11
Apr7-12, 08:17 PM
P: 312
Quote Quote by genericusrnme View Post
I'd say go for the L&L book, get used to lagranges equations of motion (possibly hamiltons too, I can't remember if they come up in the continuum mechanics book) and the rigid body motion to get you used to working with stuff and then start on the intro to tensor calc/continuum mech
The equations of motion come up in heinbockels book and they aren't very well explained so you'll need to know about them before you start.
Thank you very much for your advices.
genericusrnme
#12
Apr7-12, 08:18 PM
P: 615
Quote Quote by sunjin09 View Post
Thank you very much for your advices.
No problem buddy, good luck!
sunjin09
#13
Apr16-12, 04:12 PM
P: 312
Quote Quote by genericusrnme View Post
No problem buddy, good luck!
I picked up L&L, it was surprisingly concise (as in contrast to Goldstein which frustrated me at one point of my life). Thank you.
Andy Resnick
#14
Apr17-12, 08:12 PM
Sci Advisor
P: 5,523
Quote Quote by sunjin09 View Post
<snip> I'm interested in learning about continuum mechanics, having in mind the applications in the applied field of seismology<snip>
http://www.google.com/url?sa=t&rct=j...NvWcGEywny9nkw
sunjin09
#15
Apr18-12, 03:26 PM
P: 312
Hi Andy, are you familiar with the field of seismology? I'm interested in seismic inverse (imaging) problems. Do you know any resources regarding research careers in this direction?


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