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For a long time I have been wondering if there is some reference in which the motion of a rigid motion is systematically studied from a mathematical perspective; i.e., without using the conventional physical methods such as relative motion and geometric mechanics.

Briefly speaking, I'm looking for a book which studies the motion of rigid bodies with differential geometry, and avoids the heavy use of physical principles.

Adrian Keister
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painday
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  • Why do you want to avoid Physics?! – CroCo Apr 16 '18 at 15:46
  • Because I have some difficulties digesting the basic physical principles, in other words, ( I know that this is not good) I don't like human's physical intuition, or something like that... – painday Apr 16 '18 at 15:51
  • I don't trust human's physical intuition? you're kidding, right? – CroCo Apr 16 '18 at 15:53
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    If you're looking for a mathematical treatise that builds analytical mechanics sufficiently from the ground up, I couldn't recommend Lanczos's Variational Principles of Mechanics highly enough. – Michael L. Apr 16 '18 at 15:53
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    There are several ways to compute the equations of motion for a rigid body. A popular and rigerous physical principle is based on the Lagrange equations (c.f. Lagrangian mechanics). Try, for example, 'Classical Mechanics of Particles and Rigid Bodies' - Gupta. – Damien Apr 16 '18 at 15:54
  • @Croco: In fact I am skeptical about the laws derived from the numerous experiences , since they are the result of practical observations. However, one might argue that mathematics is to some degree also an artificial work of human's brain, but I still prefer maths, since it's more self-consistent. – painday Apr 16 '18 at 16:02
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    This is not exactly what you're asking for, but you may want to look at Osgood's Mechanics (1937). (Yes, this is the Osgood who came up with a Jordan curve having positive measure, the Osgood who essentially came up with the Baire category theorem independently of Baire, etc.) There is also a 1951 English translation (continued) – Dave L. Renfro Apr 19 '18 at 10:33
  • of Banach's textbook on mechanics (Polish original published in 1938) --- see the bottom of this web page for .pdf files of the chapters. (Yes, this is the Banach you're thinking of!) The reason I mention these two books is that they are likely to be careful with various mathematical aspects of the subject. I say "likely to be" because, although I've known about these books for many years, I have not examined them very closely. – Dave L. Renfro Apr 19 '18 at 10:38
  • @Dave L. Renfro: Many thanks! These two books really help a lot. – painday Apr 19 '18 at 15:20

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