This book provides an introduction to geometric algebra as a  unified language for physics and mathematics. It contains 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  textbooks. These methods have been widely applied in recent years to  biomechanics and robotics, to computer vision and geometric design, to  orbital mechanics in government and industrial space programs, as well  as to other branches of physics. The book applies them to the major  perturbations in the solar system, including the planetary  perturbations of Mercury's perihelion.   Geometric algebra integrates conventional vector algebra (along with  its established notations) into a system with all the advantages of  quaternions and spinors. Thus, it increases the power of the  mathematical language of classical mechanics while bringing it closer  to the language of quantum mechanics. This book systematically  develops purely mathematical applications of geometric algebra useful  in physics, including extensive applications to linear algebra and  transformation groups. It contains sufficient material for a course on  mathematical topics alone.   The second edition has been expanded by nearly a hundred pages on  relativistic mechanics. The treatment is unique in its exclusive use  of geometric algebra and in its detailed treatment of spacetime maps,  collisions, motion in uniform fields and relativistic precession. It  conforms with Einstein's view that the Special Theory of Relativity is  the culmination of developments in classical mechanics.

New Foundations for Classical Mechanics PDF

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