Physics
All the physics algorithms implemented in Springysim are described in a series of papers by Andrew Witkin, David Baraff and Michael Kass. The papers are freely available here.If these links become unavailable, Googling “Introduction Physically Based Modeling” should turn up something.
Andrew Witkin and David Baraff also taught a course in 1994 at Carnegie-Mellon covering the same material. The course notes are still available here. Many thanks to the authors for making these very interesting documents freely available. In addition to the course notes, the course assignments are available. Completing these serves as a great introduction to these topics.
A certain level of mathematical ability is required to understand these papers, but not that much. First-year university mathematics, particularly matrix theory and basic differential equations should be adequate.