New foundations for classical mechanics
by David Hestenes · first published 1986
63% recommend38% neutral
Why HN recommends it
Reference on applying geometric algebra to classical mechanics. Readable and well regarded, suited to physicists and programmers seeking a geometric algebra application.
Summarised by Claude from recommending comments
"This book provides an introduction to geometric algebra as a unified language for physics and mathematics. It containes extensive applications to classical mechanics in a textbook format suitable for courses at an intermediate level. The text is supported by more than 200 diagrams to help develop geometrical and physical intuition. Besides covering the standard material for a course on the mechanics of particles and rigid bodies, the book introduces new, coordinate free methods for rotational dynamics and orbital mechanics, developing these subjects to a level well beyond that of other textbo
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…from a mathy perspective, try Chisolm’s [book-like thingy on arxiv][chisolm] If you want a whole book of concrete problems to solve at an advanced undergraduate physics student level, try Hestenes’s [New Foundations for Classical Mechanics][nfcm]. This is the best source I’ve seen anywhere about understanding complex rotations in mechanics problems. If you want to solve some plane geometry problems, this thing looks fairly accessible [Treatise…
on “Clifford Algebra: A visual introduction (2014)” ↗…highly recommend studying his work on modeling, as well as studying his work on Geometric Algebra. That is, every physicist, especially mechanics teachers at the undergrad level, should try working through New Foundations for Classical Mechanics, and every physics teacher at every level should spend some solid time with http://geocalc.clas.asu.edu/html/Modeling.html http://modeling.asu.edu/ As for coordinates: there are many many problems in…
on “Reforming the Mathematical Language of Physics (2002) [pdf]” ↗My personal recommendation for a book on geometric algebra is the one by Hestenes, New Foundations for Classical Mechanics (https://www.amazon.com/dp/0792355148/). I was disappointed by Geometric Algebra for Computer Science and I recently got rid of my copy when I moved to a new apartment, but I have a mathematics background…
on “Less Weird Quaternions Using Geometric Algebra” ↗…hardware. I think the day is coming for an explosion of GA in everything, since it has been simmering behind the scenes for many years thanks to many, Dave Hestenes[2] in particular. I love his book New Foundations for Classical Mechanics. I program in APL and J[3], and hope that the array programming will segue into a winning GA library/module and way of approaching coding GA to make it more of a player in my work rather than my hobby.…
on “Exploring Physics with Geometric Algebra, Book I [pdf] (2016)” ↗…https://www.shapeoperator.com/2016/12/12/sunset-geometry/ And perhaps follow up with the GA for Computer Science book, or if you like (or want to learn about) Newtonian mechanics, try Hestenes’s book New Foundations for Classical Mechanics. For people with a mathier background, I would recommend https://arxiv.org/abs/1205.5935
on “Seven-Dimensional Cross Product” ↗> Suppose I want to teach first-semester mechanics If you need to teach undergraduate mechanics, I highly recommend you at least read some of Hestenes’ New Foundations for Classical Mechanics http://geocalc.clas.asu.edu/html/NFCM.html > without any distinctive advantages The most basic distinctive advantage is that you can invert vectors (which is incredibly useful!!) without needing to…
on “What is the inverse of a vector?” ↗…any field to spend too much of your time refactoring, however advantageous it might be for humanity in the long run. If you’re interested in physics applications, you should check out Hestenes’s book New Foundations for Classical Mechanics, which is pretty good. I’m particularly impressed with the completeness of the treatment of rotations and rigid body mechanics in chapters 5 and 7. General relativity is a field where Geometric Algebra…
on “Clifford Algebra: A visual introduction (2014)” ↗…http://geometry.mrao.cam.ac.uk/wp-content/uploads/2015/02/Im... “Geometric Algebra” http://arxiv.org/pdf/1205.5935v1.pdf (this one is a good place to go if you get stuck in another source). (Or books might be better sources for going in depth. Search for New Foundations for Classical Mechanics, Geometric Algebra for Computer Science, Geometric Algebra for Physicists) You’d also probably enjoy Hestenes’s work on modeling in physics teaching, e.g. http://modeling.asu.edu/R&E/ModelingThryPhysics.pdf http://worrydream.com/refs/Hestenes%20-%20Modeling%20games%2... http://modeling.asu.edu/R&E/Notes_on_Modeling_Theory.pdf http://modeling.asu.edu/R&E/Hestenes-ModelingTheory2007.pdf
on “Learn Difficult Concepts with the ADEPT Method” ↗…Algebra, by Alan Macdonald: http://www.faculty.luther.edu/~macdonal/laga/ Vector and Geometric Calculus, by Alan Macdonald: http://www.faculty.luther.edu/~macdonal/vagc/index.html Application to physics: New Foundations for Classical Mechanics by David Hestenes: https://books.google.com/books/about/New_Foundations_for_Cla... Geometric Algebra For Computer Science by Dorst, Fontijne, and Mann: http://www.geometricalgebra.net/index.html
on “Introduction to Clifford Algebra (2006)” ↗…elementary level. You could try Alan MacDonald’s book Linear and Geometric Algebra which is designed as an intro undergraduate textbook. If you want to also learn some mechanics, you could try Hestenes’s book New Foundations for Classical Mechanics.
on “Symplectic Geometry in 2D – Points, Lines, Circles” ↗In case it helps: In addition to "Geometric Algebra for Physicists" (whose first two chapters I'd recommend to get a nice overview), I found Hestenes' "New Foundations for Classical Mechanics" to be very good and readable. Also, there are many good resources in https://bivector.net/ , including videos, papers, presentations and programs. Finally, an interesting paper (that got me kickstarted)…
on “Ask HN: Math books that made you significantly better at math?” ↗That one is by Doran and Lasenby. Hestenes wrote: New Foundations for Classical Mechanics.
on “What is the inverse of a vector?” ↗…Alternatively, they could calculate the magnetic field using geometric algebra, and express it as a bivector, at which point all of those special rules vanish. That's why Hestenes's book is called "New Foundations for Classical Mechanics". It's not that linear algebra is not the foundation for geometric algebra. It's that classes taught in colleges which are called "linear algebra" teach you the concepts used by Gibbs and Wilson in the…
on “Less Weird Quaternions Using Geometric Algebra” ↗I have been studying GA ever since first hearing about it 10 years ago. David Hestenes book, "New Foundations for Classical Mechanics" was my first foray followed by "Geometric Algebra for Physicists" by Doran and Lasenby, however lately I have been focusing a on GA for computer graphics instead of physics. I am working through Euclid's…
on “A Bigger Mathematical Picture for Computer Graphics [video]” ↗…what you are looking for (notations used, etc) is possibly here: http://geocalc.clas.asu.edu/html/Evolution.html#References under "Recent Books". Notably "Clifford Algebra to Geometric Calculus" and "New Foundations for Classical Mechanics" by Hestenes. PD: if you ever attempt to read any of those two, I'd advise to go to the latest (corrected) reprint.
on “Let's remove Quaternions from every 3D Engine” ↗