Reference request - book on Euclidean space and rigid body kinematics Ideally, I'd like a comprehensive book that encompasses both subjects: it builds the notion of "space" as related to our physical world (no relativity, though) from the ground up, giving it mathematical rigor (admittedly I am not sure if Euclidean space is in fact what I am looking for), and then develops the theory of rigid body motion, with formal treatments of the different types of motions, such as translational and rotational. There's no need for the book to tackle the kinetics of these motions. Obviously, if it's in there, I won't complain.
Do you know of anything that might fit this description?
 A: William Heard's Rigid Body Mechanics: Mathematics, Physics and Applications seems to fit the bill but there are some heavyweight parts on tensors and quarternions right from the beginning... if you need any more abstraction on geometrical nature of classical mechanics you can always go to Abraham & Marsden Foundations of Mechanics
A new, easier and very decent book I've seen recently is Helliwell & Sahakian Modern Classical Mechanics which discusses a lot of intuition, but of course is not limited to those topics you mentioned.
A: If you're familiar with Real Analysis, solving Ordinary Differential Equations and Linear Algebra, then the best reference is Arnold's classic Mathematical Methods of Classical Mechanics. Due to its brevity, it may be a hard book to follow at times. A great complementary resource would be Spivak's Physics for Mathematicians, Mechanics I, which has some great historical context and attention to physical details. He fleshes out pretty much the same material in much more detail. Not to mention, Spivak's books generally have great problems to solve. It does assume some knowledge of Differential Geometry, especially the later parts. However, Arnold's book would teach you the bare minimum necessary, when it becomes so and hence is a much better primary resource to use.
