13.3.1 The Newtonian Model

The most basic formulation of mechanics goes back to Newton and Euler,
and parts of it are commonly studied in basic physics courses.
Consider a *world* defined as in Section 3.1, except
here a 1D world
is allowed, in addition to 2D and 3D
worlds. A notion of time is also needed. The space of motions that
can be obtained in the space-time continuum can be formalized as a
Galilean group [39]; however, the presentation here will
utilize standard intuitive notions of time and Euclidean space. It is
also assumed that any relativistic effects due to curvature of the
time-space continuum are nonexistent (Newton and Euler did not know
about this, and it is insignificant for most small-scale mechanical
systems on or near the earth).

Steven M LaValle 2012-04-20