Book on coordinate transformations

Question

I am looking for a book that covers various coordinate systems in 3 dimensions, various methods of representing rotations and other transformations like rotation matrices and quarternions, including algorithms for conversions between various coordinate systems and representations of transformations. Is there a single book that covers these.

Answer 1

I do not know a book that covers all aspects.

• In mathematical introductions for physics and engineering you will find Cartesian, cylindrical and spherical coordinates mostly, because it will help to solve problems with cylindrical and spherical symmetry.

• Books on mechanical engineering or theoretical mechanics will introduce Euler angles for the modeling of rigid bodies. Note gimbal lock.

• Books on robotics often treat the modeling of a robotic arm and will provide useful representations for that application, including use of quaternions.

• Books on computer graphics will feature homogenous coordinates, to handle affine transforms in matrix representation. For general barycentric coordinates see e.g. Barycentric coordinates

• Books on geographical information systems or geodesy have to deal with the fact that the earth's surface is not flat and give useful coordinate systems and operations.

• Mathematical books on multidimensional calculus or differential geometry will teach you the general cases. They build on analytical geomery and linear algebra.

• Books on aviation and space exploration might have their own specialities to handle navigation. E.g. see ICRF.