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The Shaggy Steed of Physics 181

Posted by timothy
from the smarty-jones-is-dumb dept.
Sarusa writes "The Shaggy Steed is an Irish folk tale about a prince whose kingdom has fallen into chaos. A druid provides him a small shaggy horse which guides the prince on his quest through great trials and tribulations to a magical realm where he can obtain the necessary powers with which to bring peace to his land. (You can find more detail here.) For David Oliver, the Shaggy Steed of Physics is the two-body problem: the motion of two bodies bound together by the inverse square law." Read on for the rest of Sarusa's review of Oliver's book The Shaggy Steed of Physics. Fair warning: the review is lengthy, because the book demands it.
The Shaggy Steed of Physics: Mathematical Beauty in the Physical World
author David Oliver
pages 300
publisher Springer
rating 8 of 10 (if you have the required math skills)
reviewer Sarusa
ISBN 0387403078
summary Beautiful but demanding examination of the two-body problem.

The force on each body, whether gravitational or electric, is proportional to the square of the distance between the bodies. An isolated sun and planet form such a system, and a hydrogen atom, which is just a proton and electron, can be simplistically modeled as such. This may seem a trivial problem: you can sum it up in half a page in a physics book. But that's because all the detail work has been done for you. Furthermore, anything more complex than the two-body problem is chaotic and incapable of exact solution, so it's up to the two-body problem to carry us along. This is a complex problem, so this review is rather lengthy.

Let me warn you right off the bat that this is not a book for the faint of heart. It kicked my ass. The concepts are fast and furious, and the math is dense. Equations festoon the pages, daring you to ignore them. But you may not, they're fundamental to the discussion. Mr. Oliver opines that anyone with basic undergraduate math should be able to handle it. I had calculus, differential equations, and a good dose of physics in college and I still found the book tough going, mostly due to the whirlwind of notation and sheer number of variables introduced. I ended up keeping a cheat sheet of key definitions which ended up being four pages long, and took almost two weeks to process it. It reads like an advanced college physics book, except without extra examples or redundant explanation -- he expects you to be smart or motivated enough to keep up.

As an example: 'Using Hamilton's equations to eliminate p' and q', the total rate of change may be compactly expressed as df/dt = df/dt + [f,H] where [f,g] is the Poisson bracket of any two functions of the motion: [f,g] = (df/dqi*dg/dpi - dg/dqi * df/dpi)' I've reformatted this slightly for text limitations; he of course doesn't use * for multiplication, and you should read all 'i's as subscript i. This is fairly simple math in the context of the book.

So now that I've scared you off, what's the payoff? Well, unlike my college physics books which just lead me from factoid to factoid there are moments where the hard work pays off in big "oooh" moments. Your book might give you Kepler's second law: a planet sweeps out equal areas of its ellipse in equal times. But why? We'll just call it 'conservation of angular momentum'; that should hold you plebes. But in Shaggy Steed you'll find the equations like this that you might have thought were fundamental falling out of the woodwork, built up from the real fundamentals.

We start out by defining coordinate spaces and deciding that we're interested in Newtonian/Galilean rather than Einsteinian physics for the moment, since our subjects travel slowly enough and relativity makes things nastier. We start with a particle that has two vectors -- position and velocity. Turn this into two ensembles of rigid body particles exerting force upon each other. From this we build up the laws of motion, arriving at the total energy H of the system, and the 'gene of motion,' the Lagrangian: the difference between the kinetic and potential energy. 'Gene of motion' is a pretty bold claim, so we are shown how every mechanical quantity of the system may be derived from the Lagrangian. From there it's on to the 'action' principle, which is basically the integral of the Lagrangian over time - the key being that of any path the particles may take, they act in a way to minimize the action. Every other law of motion (including Newton's) follows from this, though to explain why it's the case we need general relativity. This was my first 'oooh' moment.

Chapter 3 really sets the pace for the rest of the book. If you're thrown off here, you're not going to make it out alive. To summarize: "Motion consists of the trajectory flow of particles in phase space. Each isolating invariant introduces a degeneracy into the motion in which the full phase space available to the trajectories degenerates into a submanifold. Increasing numbers of isolating invariants correspond to increasing degeneracies of the motion which restrict the trajectories to increasingly restricted submanifolds of phase space." This is more or less the programme of the entire book. Dig out as much complexity as required, then simplify to solvability.

Oliver introduces each new concept, so if you're following along carefully, you can follow along. This is all done half in equations, so we're diving so deep into math that you (okay, I) may be several pages in and forget where you were coming from and where you were going. Then suddenly you're out the back end and he nails it all with a beautiful concrete application or insight. For Chapter 3 it's Hooke motion, which you can think of as approximating two weights connected by a spring. Now if you've ever taken differential equations, or dynamics, you're probably uncomfortably familiar with this system. Now here it is all laid out for you, everything explained, and boy those resultant equations look mighty familiar. So that's where that all comes from, and why they use those particular symbols. The linear central force and the inverse-square forces of our two-body problem turn out to be closely related as well.

To be crushingly brief, Chapter 4 finally gets down to the (relatively) practical matter of classical planetary (Keplerian) mechanics, and why four dimensional spheres are special. Chapter 5 dives into quantum mechanics, and the hydrogen atom loosely simulated as a two body problem, since it has only the nucleus and one electron. And let's derive the fundamentals of quantum physics and the periodic table while we're here. Though I've neglected to mention it till now, Oliver doesn't neglect the human side of all this. He doesn't linger on it, but he does provide context. It's amusing to see how many of these inexorable equations were originally derived by geniuses like P. Dirac, only to be disowned because the implications were too outlandish.

In Chapter 6, it's time to step out of Newtonian/Galilean space and into Einsteinian space. We've made a lot of assumptions, such as the infinitely fast propagation of forces. This is no longer the case; time is no longer separate from space. In fact, we learn how to rotate space into time through imaginary rotation angles (known as 'boosts'). e=mc^2 falls out. But our shaggy steed eventually breaks down on the precession of Mercury. In the land of general relativity, even a simple two-body problem is really a many-body problem - forces are no longer instantaneous, they require force particles. The steed is of no more use.

But wait! Chapter 7, The Manifold Universe, takes on many-body motion like Don Quixote tilting bravely at a windmill, and tries to pull some order from the chaos. KAM theory is introduced and our many-body problem turns out to be not absolutely chaotic, but a mixture of regular and chaotic motion. You may have noticed that our many-body solar system doesn't just fly apart. We can model it more or less as a set of two-body problems with minor perturbations (minor being the key). And of course we can model fluids even though the internal motion is chaotic. Order emerges. Our shaggy steed is revived, transformed.

The back of the book contains the Notes, which are compact digressions into the hard (yes ...) math. I have to admit some of them completely lost me. But they're not required, just extra reading for those of you who eat this stuff up.

This all leaves me with a bit of a quandary. It's a beautiful book if you're a graduate-level student of math or physics, smarter than me (your best bet), or willing to put a lot of effort into it. Otherwise I can't recommend it -- the book is gibberish if you can't follow the math. I can't help but think that it would make a fantastic course in the hands of a skilled practical math teacher like Dr. Gary Sherman at RHIT; I certainly could have used his help with this. So, it's to teachers like him that I'd really suggest this book, for eventual dissemination to their students. Or if you dig physics and have the math skills, you might want to try riding "The Shaggy Steed of Physics" alone. If it throws you, there's no shame.


You can purchase The Shaggy Steed of Physics: Mathematical Beauty in the Physical World from bn.com. Slashdot welcomes readers' book reviews -- to see your own review here, read the book review guidelines, then visit the submission page.

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The Shaggy Steed of Physics

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  • by D3 (31029) <daviddhenning&gmail,com> on Tuesday September 14, 2004 @05:35PM (#10250318) Journal
    Fair warning: the review is lengthy, because the book demands it.

    Yes, I believe on the inside cover the book EULA stating "All reviews of this material must be over 3 pages in length"
    • That's not half as bad as the EULA in the new PARANOIA XP rulebook [amazon.com].

      Hell, the termination clause of it is "you may be terminated" ;] I think you also give up your rights to liberty, the persuit of happiness, and Bouncy Bubble Beverage in there somewhere, too, but my memory seems to have been erased in order to better server Friend Computer...
  • by Anonymous Coward
    SPOILER! Scroll down to read below.





    Although there are some places that could be better, I give this book an 8 out of 10.

  • by tcopeland (32225) * <tom@[ ]masleecopeland.com ['tho' in gap]> on Tuesday September 14, 2004 @05:38PM (#10250334) Homepage
    ...is O'Reilly's Physics for Game Developers [oreilly.com].

    One of the chapters - on 'real world' projectile motion - is available for download at the above site, so you can get a feel for the writing and content.
    • by johnnyb (4816) <jonathan@bartlettpublishing.com> on Tuesday September 14, 2004 @05:46PM (#10250392) Homepage
      I thought game developers got to make up their own physics :)
    • Too light (Score:5, Interesting)

      by Animats (122034) on Tuesday September 14, 2004 @06:24PM (#10250655) Homepage
      Speaking as the author of a physics engine for animation [animats.com], "Physics for Game Developers" is a bit too light for an engine developer. The easy stuff (i.e. what you'd get in a college-level dynamics course) is covered, along with collision detection. But beyond that, the book does not take you.

      Basic problem with building a game physics engine: if you do all the obvious stuff, it sort of works. If you're competent, you should be to that point in a few months. Getting from "sort of works" to "works" is about 5x to 10x as hard as the first step. There are really only a few game physics engines out there that really work.

      You'll find out more about stiff systems of nonlinear differential equations than you ever wanted to know, if you don't give up first.

      It's interesting that the book talks about the problems that occur when you take into account the propagation delay of gravity. Game physics engines, having rather large time steps, have some similar problems. I'll have to read this and see if I get any new insights applicable to game engines.

      There's a related book, an ACM prizewinner, on the N-body problem. There's a clever numerical solution to the N-body problem that works for large N (millions), so you can simulate galaxies forming and such. The basic idea is that you can treat a group of bodies as a single body if they're near to each other and far away from the body being affected. This can be quantified and safe limits computed for grouping. It's thus a numerical solution with a proveable upper bound on the error, which bound can be made arbitrarily small at the cost of more computation. This is effectively as good as a closed-form solution, although some older mathematicians deride it as inelegant.

  • Long review? (Score:4, Insightful)

    by tinla (120858) on Tuesday September 14, 2004 @05:39PM (#10250340) Homepage Journal
    Maybe I'm in a minority of 1, but that review didn't seem very long to me. Sure its longer than a jacket summery... but it hardly does as far enough to be in-depth let alone deserve a warning.

    anyway... better than the usual 'contents table' affair we get on slashdot I suppose. Hardly Sunday paper review long though.

    • "didn't seem very long to me. Sure its longer than a jacket summery..."

      well, i would have seemed longer if you'd been wearing a parka wintry.

  • by erick99 (743982) <homerun@gmail.com> on Tuesday September 14, 2004 @05:40PM (#10250354)
    For folks like myself who would like to know more about what the book covers, but is not going to spend several weeks working through the math and learning math. Perhaps the content goes beyond what can be known without doing the math, I don't know. Hell, how could I?

    Cheers,

    Erick

    • by AuMatar (183847) on Tuesday September 14, 2004 @05:57PM (#10250473)
      Are you looking to learn physics or understand physics? You can have Kepler's laws explained to you in a page or two, and learn enough to use them in basic ways. TO understand physics, you need to do the math. If you don't, you can memorize a bunch of equations but you'll never understand where those equations come from.
    • If you want a rough idea of the physics involved without the math, then you can probably just read the book, skipping the equations as they come to you. This way you'll still wind up getting the concepts as they're explained. Of course if you do this you're missing out on the overall beauty and spirit of physics, but at least you'll get a sense of what's going on. It's kind of like reading Shakespeare's Hamlet directly vs. reading a summary of it.

      The book's content seems to be the basics of classical m

  • by halivar (535827) <{moc.liamg} {ta} {reglefb}> on Tuesday September 14, 2004 @05:42PM (#10250365) Homepage
    Otherwise I can't recommend it -- the book is gibberish if you can't follow the math.

    If you want it to make sense, you gotta accept the fact that the book, by itself, is not supposed to turn an interested laymen into a learned professor. Books like these, for me, spur me to go learn the basics instead. Even if I never get all the way through the book, I can at least use it to tell me what I need to know to be considered "learned" in the field.

    I remember in college as a CS student, being spoon-fed the easy-to-learn computing theory and feeling like I was getting nowhere. I picked up the Hopcroft & Ullman automata book and was, at the time, completely inundated by the math (I went to a commuter college with a not-so-advanced math & CS dept.). But at least I knew what I really needed to learn next. I ignored the professor pretty much for the rest of the class (and never opened the textbook) and instead investigated only those things I required to understand the H&U book. I found that by the end of the class, though I was not yet a quarter of the way through the book, I knew a lot more than my classmates, who still struggled with the basic concepts of the field.

    If the book seems too much for anyone other than an grad student, try using it instead as an index of things you need to learn first. Don't know those formulas? Look 'em up. Even if you don't grasp everything in your target book, you'll be smarter for it in the end.
    • by Tired and Emotional (750842) on Tuesday September 14, 2004 @06:03PM (#10250517)
      > Otherwise I can't recommend it -- the book is gibberish if you can't follow the math.

      I wonder if this is worse than the science popularizations (esp in physics) that are gibberish because they contain no math.

      I know I treat a physics book that does not have at least one equation a page with deep suspicion.

      One of my favorite physics books is Misner Wheeler and Thorne's "Gravitation". Not only is it full of math, but you can use it experimentally as a gravitational field generator.

  • RTFS - Read The Frelling Summary

    Man, I was thinking this was an awesome book, but after scrolling through like 2 pages of the summary, I felt like I had been hit by a truck

    Refer your friends, get an ipod [tinyurl.com]
  • by MikeMacK (788889)
    Otherwise I can't recommend it -- the book is gibberish if you can't follow the math.

    Pretty much sums up most physics books I've ever seen.

    • Re:Most of them (Score:3, Interesting)

      by rokzy (687636)
      you obviously haven't seen "A Brief History of Time", "In Search of Schrodinger's Cat", "Schrodinger's Kittens" and many other non-maths physics books.
      • I've heard of them, unfortuneately my professors obviously haven't.
      • Re:Most of them (Score:4, Insightful)

        by Christopher Thomas (11717) on Tuesday September 14, 2004 @06:00PM (#10250498)
        you obviously haven't seen "A Brief History of Time", "In Search of Schrodinger's Cat", "Schrodinger's Kittens" and many other non-maths physics books.

        These are "physics books" the way "the matrix" is a computing and AI primer. That is to say, they tell you that several of the important concepts exist, in a way that's entertaining, but don't do much to tell you how to actually _use_ them.

        At best, "physics overview for the layman", as opposed to "physics reference".
      • as a physist I enjoyed reading "A Brief History of Time" because I know a bit about the physics behind it at enjoyed the conversational tone of the books. Yet, I think without this background this book would just have given me very strange ideas about the universe "lies to children" as Terry Pratchett is fond of calling it. There is only so much that can be truely comprehended without Mathematics.
    • i read this one... true to the form of physics books, there was an unexpected plot twist at the end.

      it turns out everything we thought we knew and backed up with math and logic, was wrong. beware of the guy at the end of the universe, i hear he's real strict on who gets in...
      • I thought it was really easy to get into Milliways. And then all sorts of neat stuff happens- the cow comes by and asks what steak it can donate for your dinner, and later on the universe will be ending for your entertainment.
    • Re:Most of them (Score:5, Informative)

      by wass (72082) on Tuesday September 14, 2004 @07:35PM (#10251227)
      The reviewer raves about this book (despite not recommending it at the end), but IMHO misjudges the level or prerequisites of the reader that this book might interest. I'm a graduate physics student who didn't read this book (actually I never heard of it until now), but I'd like to throw in some comments that differ from those of the reviewer.

      This book sounds pretty cool, but I disagree with the reviewer regarding the level of the book, which I can gauge from the reviewer's comments. The reviewer tends to think it's well beyond advanced undergraduate physics classes, but from the material involved I think it's somewhere between the intro and advanced undergrad classes. It sounds like this book would be useful for armchair physicists that would like to get their hands a little more dirty, people minoring in physics, and physics majors wanting a little more 'oomph' before their 'real' classes kick in. But IMHO, one definitely shouldn't need to be a grad student in math or physics to enjoy this book as the reviewer implies.

      For example, the reviewer writes "It reads like an advanced college physics book, except without extra examples or redundant explanation -- he expects you to be smart or motivated enough to keep up."

      So upon reading that one assumes the reviewer at least took some decently advanced calculus-based physics classes well beyond the freshman level (like a two-semester class of E&M or quantum mechanics, or classical mechanics).

      But then the reviewer says "Your book might give you Kepler's second law: a planet sweeps out equal areas of its ellipse in equal times. But why? We'll just call it 'conservation of angular momentum'; that should hold you plebes. But in Shaggy Steed you'll find the equations like this that you might have thought were fundamental falling out of the woodwork, built up from the real fundamentals."

      This quote right here reveals that the reviewer hasn't been exposed to any 'advanced' physics classes, maybe just advanced introductory ones. Only the intro classes will 'tell' you about Kepler's 2nd law and conservation of angular momentum. This concept, though, is usually proved and derived from the fundamentals in any reasonable undergraduate physics mechanics class beyond the freshman-level class. Such an undergraduate level mechanics class would, for example, use the textbooks by Arya or Marion/Thornton.

      Similarly with motion in phase space, simple harmonic motion, Lagrangian equations of motion, the energy eigenstates of the hydrogen atom (this would be in the quantum mechanics class), etc. These are all topics which are examined from the fundamentals, and encountered usually within the first two or three years of an undergraduate physics curriculum.

      So the Shaggy Steed is a book somewhere beyond the intro physics classes, but not as difficult as the more advanced undergraduate physics classes, where the majors start going. Note - if you really like this low-level sort of stuff, though, you might seriously consider majoring or minoring in physics.

      So I disagree when the poster writes "It's a beautiful book if you're a graduate-level student of math or physics..." Most of the material covered seems to be the standard fare that the typical undergraduate physics major will encounter, and some of these topics will likely be encountered several times prior to graduation.

  • Perhaps I'm behind the times, but aren't gravitational force-carrying particles simply conjecture at this point in time? Yes, they're logical and fit nicely into our understanding of the three [four] fundamental forces, but they aren't scientific fact yet by any means of the term - perhaps at most a theory that makes sense, but we've found impossible to test. But like I said, maybe I'm just behind the times.
    • Seydlitz says:

      Perhaps I'm behind the times, but aren't gravitational force-carrying particles simply conjecture at this point in time?

      I think so too, but if you consider vibrations and waves in a ten-dimensional space as that which makes up the universe, any "particle" is a concept that is optional.

      As long as you can't decently manipulate and measure the particle, I guess it up to your feeling of aesthics which model you follow.

      I personally believe in: God isn't rolling dice, God is playing billard.

    • Re:Small nit-pick (Score:3, Informative)

      by Chuckstar (799005)
      Gravitons (the gravitational force carrying particles) are still very much hypothetical. They are postulated merely because all other forces seem to have a particle that carries them. Certain quantum theories of gravity require them, but no one has a really good quantum theory of gravity yet anyway. However, the fact that gravity does not act instantaneously has been observed. So there does need to be some way to propogate gravity from one location to another. There does need to be some type of wave, p
      • "the fact that gravity does not act instantaneously has been observed"

        wasn't it originally *deduced* before observation, by Einstein I believe?
        seems to me I recently saw this on PBS (in a show about string theory) -- something about a gedanken experiment about the change in the Earth's path if the sun vanished instantaneously, and how instantaneous gravity would be contradictory with non-instantaneous light.

        btw, it's "propAgation"
  • Anyone here care to explain to someone not yet finished with higher level maths.....?
    • Layman's translation (Score:3, Informative)

      by Dhaos (697924)
      Ok, a little layman summary:

      There's a fairly easy problem in physics. It's called the two-body problem. In it, you model (or predict) the motion of two objects in space as dictated by the force of gravity.

      It's based on the Newtonian equation for gravity, which is that the force of gravity acting on two objects is proportional to the square of their distances. To put this more simply, the force of gravity between two objects gets drastically weaker as they are moved farther away.

      All that being said,
      • You neglected the important fact, made strongly in the review, that the first half of the book is devoted to deriving the commonly known equations, including Newton's,, that govern the two-body problem.

        I want very strongly to read this book....
  • by MikeMacK (788889) on Tuesday September 14, 2004 @05:53PM (#10250442)
    The Arch-Druid then instructed him thus: "Take," said he, "yonder little shaggy steed, and mount him immediately

    Kind of inappropriate if you ask me.

  • by Doc Ruby (173196) on Tuesday September 14, 2004 @05:54PM (#10250453) Homepage Journal
    I glean from the review that the book is a detailed examination of the two-body model for object interactions, from femtoscopic to macroscopic, in the original, untranslated mathematical language. But what has all that got to do with a small, shaggy horse? I can guess from the Slashdot summary that the model is like the small Irish steed, guiding its rider to exciting, unknown places. But does that mean that the long review isn't as relevant to a synopsis as the Slashdot summary, and that the first line of this post is the capsule review proclaimed impossible by the reviewer?
  • Ohh, I am salivating already! Thanks for the reference!!!
  • by Sialagogue (246874) <sialagogueNO@SPAMgmail.com> on Tuesday September 14, 2004 @06:00PM (#10250500)

    1,082,811
  • Mathematical Physicists tend to apply solutions to differential equations like the 2-body Shrodinger's equation as if they know how to solve an arbitrary differential equation. This type of posturing is probably the kind that you see in this book. The problem being described is actually found in just about every undergraduate modern physics textbook and every physical chemistry textbook. The way mathematical physics is delivered to an audience usually sends them as far away from the subject as possible.
    • Not all. I had a physics prof who was married to a math prof. They both have their own research areas that scare the heck outta me with the math, but know how to tone it down to undergrads. My undergraduate courses got overhauled and replaced by a new pilot program that breaks the work up into problem types. This makes mathmatical physics much easier to deal with then subject area. Rather than skipping to the hardest parts 'cause you gotta finish mechanics before em' you go in a much more sensible manor. We
    • Mathematical Physicists tend to apply solutions to differential equations like the 2-body Shrodinger's equation as if they know how to solve an arbitrary differential equation.

      Gosh, I wonder what the artistic physicists think...
  • The exemplary equation does not make much
    sense as it is and should really be:
    df/dt = \partial f / \partial t + [] ...

    I am using LaTex notation where \partial t is the
    partial derivative with respect to t and dt is
    of course the total derivative.

    By the way, the book seems to be a solid introductory text for physics students.
    Nothing more nothing less ...
  • Im really surprised at some of these responses... i would really have expected most of you folks out there to be able to understand the chain rule and poisson notation. Granted its a little lame to be in a fantasy book, but sounds pretty interesting and a good quality review. Thats my two bits.
    • Chain rule I can see. Poisson brackets are not exactly common in the IT/CS crowd that tends to be drawn to /.

      As far as the fantasy book thing, did you bother to RTFA? This is a physics book, it has about as much to do with fantasy as Blazing Saddles has to do with Sci-Fi.
      • ok, i didnt rtfa till after i posted but still even if it is a textbook (the price shoulda gave it away...) the review didnt give hint to this fact. Only following the bnr link did i get it. Anyway, i wasnt going to read it either way.
  • by phr1 (211689) on Tuesday September 14, 2004 @06:13PM (#10250594)
    Structure and Interpretation of Classical Mechanics, by Gerald Jay Sussman and Jack Wisdom:

    MIT Press blurb [mit.edu]

    The book is also online in html form [mit.edu]. It sounds like you weren't used to the Lagrangian formulation of mechanics, which has been around for a long time but is usuually not taught in lower level undergrad physics courses (i.e. normal engineering physics). If you take an upper level class in classical mechanics, you'd cover it thoroughly. Sussman and Wisdom's book presents it in an interesting computer-inspired way. Note though that this is a textbook (with problem sets and all that), not a popularization.

  • by Aardpig (622459) on Tuesday September 14, 2004 @06:21PM (#10250639)

    Furthermore, anything more complex than the two-body problem is chaotic and incapable of exact solution, so it's up to the two-body problem to carry us along.

    Not quite; the restricted three-body problem, where one of the masses is infinitessimal compared to the other two, can be solved analytically. The solutions reveal the existence of five points where the net effective force on the massless third body vanishes -- these points being, of course, the Lagrange [wolfram.com] points familar to students of orbital mechanics.

    I'm surprised that the reviewer found so much of the material new; do college physics courses these days not include classical mechanics and the like?

    • Not quite; the restricted three-body problem, where one of the masses is infinitessimal compared to the other two, can be solved analytically.

      Not quite; your example is not a three-body problem, but really a two-body problem in disguise. The equations of motion for the two finite masses can be solved separately, since they are not influenced by the infinitesimal mass. Then the problem reduces to a single particle (the one with infinitesimal mass) travelling in a time-varying field.

  • Horse eh? (Score:1, Funny)

    by Anonymous Coward
    A druid provides him a small shaggy horse which guides the prince on his quest through great trials and tribulations to a magical realm where he can obtain the necessary powers with which to bring peace to his land.

    I guess that in this book, before the prince rides away on his horse, that we start by assuming that it's a perfect sphere...
    • ...of uniform density.

      We also assume the prince to be perfectly rigid.

      • We also assume the prince to be perfectly rigid.

        ... and his princess equally frigid,

        And that, boys and girls, is why the kingdom is up for grabs to any wooly-headed farm-boy lucky enough to snatch a pig-sticker from a watery tart!

        Too bad it took a Lancelot to thaw her out.

  • Slightly OT.. (Score:3, Insightful)

    by Capt'n Hector (650760) on Tuesday September 14, 2004 @06:27PM (#10250680)
    [f,g] = (df/dqi*dg/dpi - dg/dqi * df/dpi)

    Feel free to mod me as such, but the review reminded me how horribly mathematics is represented in a browser. Wouldn't it be great if one day we could simply type:

    <latex>
    LaTeX code goes here...
    </latex>
    • Re:Slightly OT.. (Score:3, Informative)

      by gatzke (2977)

      They do have a math markup, mathml.

      It is not real nice to use without some sort of editor to generate it. I think MathType does it in Windows.

      I think the latest Mozilla supports it:
      http://www.mozilla.org/projects/mathml/
      http ://pear.math.pitt.edu/mathzilla/Examples/marku pOftheWeek.mhtml

      Usually, it is probably better to make a pdf, but then you miss out on hyperlinks (unless you know how to stick them in your pdf)

    • Re:Slightly OT.. (Score:3, Informative)

      by infolib (618234)
      You can. If you write for Wikipedia [wikipedia.org].
  • But isn't physics built on math? And isn't math built on philosophy? And don't we still not have a good understanding of how gravity and electromagnetic radiation act? (take dark energy for one example, or the gravitational anomalies dealing with eclipses)

    So what we have is a complex system of symbology that is demonstrably incomplete? Why wouldn't I just want the easy version until somebody starts basing a calculus on something that may do better?

    BTW, does anybody know of a computer system that can creat
    • You are wrong.

      But isn't physics built on math?

      No. Physics is built on postulates, basic assumptions about the world. These postulates can be expressed in mathematical terms, and using math you can evaluate the consequences. But it has nothing intrinsically to do with math, only with logic. Math is a system of logic.

      And isn't math built on philosophy?

      Math is built on logic. Logic is considered a field within philosophy. That doesn't really mean you can say math is built on philosophy.

      And don't we s
  • by Goldsmith (561202) on Tuesday September 14, 2004 @08:57PM (#10251798)
    That your average engineer, chemist or other science-minded college-educated person is not at least comfortable with Lagrangian mechanics is a failure of physics education.

    In physics we generally don't think in terms of Newtons Laws, but rather in terms of the action and fields.

    In my view, the lower level college physics classes which teach 18th century physics are a complete waste of time (as the review points out, all those laws fall out of more fundamental principals). The engineering students who are forced to take physics are not even given the chance to learn "real" physics, and the physics and other science majors who take it will simply be told to forget it and learn a better way of thinking a year later.

    I'm always asking people in my department (I'm a physics grad student) why in the world we teach these useless classes. Generally the defense is that people wouldn't learn the concepts if we taught them the real way, that the math would be too hard, and people would get caught up in it.

    They forget what it was like as an undergrad. Physics can be hard, even old, 18th century physics. When I've taught physics, people always get caught up in the math. The best we can do is to at least teach the right way, and introduce the right concepts. The math can be taught, packaged or explained.

    There has been very little effort that I have seen to put real physics concepts in a package which is understandable by your average freshman biology student. This book is obviously no exception. It does not have to be this hard, and physics does not have to be only for physicists. Why do we insist on complicated terminology and crazy sounding descriptions?

    I know that a lot of engineers and others out there have had more modern classical physics classes. Were they any good? Was your education in physics enlightening or frusterating? These issues really bug me, and I hope some of you out there have had better than I've seen.
    • Oh? And how do you expect an undergraduate biology major to understand (say) a particle's motion? Personally, saying that we should NOT teach a=F/m (which makes sense in real life, as long as you can get around the tricky 'what IS mass, really?' issue) in favor of defining a trajectory as the path over which the action of a particle's motion is extremized is crap.
      Maybe you're saying that mathematics classes need to teach integral calculus a lot earlier, so that people can do path integrals, instead of a
      • You make some good points, especially about terminology, and they are a lot of the same points professors make to me when I complain to them about this, so I suppose you're in good company.

        I agree that telling students a particle follows a "path over which the action of a particle's motion is extremized" is crap. I also think it's crap to teach someone that a=f/m, now go plug in some numbers. I think students should be taught to minimize energies, and that force is not some mysterious quantity that's giv
        • Well, I've yet to see a book or professor who says anything remotely like "a=f/m, now go plug in some numbers." (Although, to be fair, probably a lot of students might see it that way.) My own take is that this sort of thing should be taught in a somewhat historical way, but with more emphasis on the history. For example, the fact that "an object in motion tends to stay in motion, unless acted upon, etc." is intuitive to me, but maybe that's because I've been thinking about this stuff for a large part of
    • I'm also a graduate student in physics, and I couldn't disagree with you more. Newtonian dynamics is great for the really simple problems, and these days anything more complex simply isn't going to be done analytically unless you want something specific enough that you can afford to teach yourself Hamiltonian mechanics.

      I study in Goettingen (I'm sure you know where that is.) and the mathematics department has a large hall of models of surfaces of least action, mainly done between 1900 and 1950. After the a
      • It's funny, most physicists I've talked to about this disagree with me. (Although you're the first from Europe, I have a friend at Delft who just blames my obsession on the poor US education system.)

        Perhaps what we do now is the best way, I can't really say I've seen anything better. You make some really good points.

        My only counter would be that many people are not working on simple problems anymore. The ideas of Hamiltonian mechanics would be very useful to anyone doing molecular biology or organic ch
  • by Mark_in_Brazil (537925) on Tuesday September 14, 2004 @09:54PM (#10252091)
    This sounds to me like a more advanced classical mechanics text. In my second year in college (physics major), we used Marion & Thornton's Classical Dynamics of Particles and Systems [amazon.com], which seems to be one of the standard texts at that level. I believe Symon's Mechanics [amazon.com] is another book at about the same level.
    In my first year in grad school, I took a great classical mechanics course taught by a guy who uses classical mechanics in his research on planetary systems. His name is Stanton Peale. He got semi-famous by publishing a paper just before Voyager arrived near Jupiter, saying that Io might be volcanic. He would have published it a lot sooner, but he didn't notice that orbital data on the Galilean moons are, for historical reasons, recorded differently than those for other moons in the solar system. He had therefore mistakenly calculated that none of the Galileans would be volcanic. By chance (if such a thing exists :D), he was working on another problem and noticed this. He then repeated his calculations and saw that tidal stresses on Io might be strong enough to give it a liquid interior. He had trouble getting the paper published in the short time before pictures started coming back from Voyager, but managed. As he told me, anyone can write a paper explaining why a moon is volcanic after the discovery of vulcanism on the moon, but he wanted to publish the prediction before the pictures came back.
    But I digress... in Peale's class, we used the standard graduate text on Classical Mechanics, which is Goldstein's Classical Mechanics [amazon.com].
    Both the Goldstein book and the Marion & Thornton book cover Lagrangian and Hamiltonian mechanics. Goldstein goes into more details about things like Poisson Brackets and canonical transformations.
    The Landau & Lifshitz book Mechanics [amazon.com], the first volume of the "Course of Theoretical Physics," covers much of the same material, but is quite concise. For that reason, like most of the Landau/Lifshitz (and Lifshitz/Pitaevskii, after Landau died) books, it is pretty dense.
    I'm not sure if Oliver intended to bring these things to folks other than physics majors, but who other than physics majors (and maybe the occasional math major or other science/engineering major) has enough interest in the subject to wade through the math? The math isn't all that complicated (for a physics or math major), but it's complicated enough to deter anyone not really interested in the subject. Peale's classical mechanics class was not quite a weed-out course, but it was one that a significant number of people dropped in their first year and were taking for the second time when I took it. I worked really hard in that class and ended up learning a lot. And it wasn't just the math that made it tough. But the point is that this material can be taught at a level that's challenging for grad students...

    --Mark
  • Sounds more like horror story instead of review:
    College kid reads a white paper disguised as a book; learns stuff.
  • Coincidentally, I've been looking for a book on mechanics to read.

    Why you ask?

    Well, I've got a pretty good math background and I've read some (not all) of the Feynman lectures. So while the math of advanced physics doesn't scare me (okay, it scares me a little), I lack any physical intuition.

    I wasn't quite prepared to plow through a dry 500 page book on mechanics. However, I was looking for an entertaining read.

    The reason is that mechanics is the intuition of physics. Most mathematicians can run math

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