Teaching Basic Mechanics With Computer Algebra, Sophia and Maple

(M. Lesser)

The standard approach to using computer algebra in basic mechanics courses has
been to apply a standard CAS such as Maple to carry out calculations in
calculator mode or with some programming built around the specific example or
problem being examined.  Another approach is to use the CAS as a foundation on
which one builds a tool kit of routines that allows the student to set up the
algorithm for the solution of general classes of mechanics problems. Sophia is
the name of such a tool kit, developed at the Royal Institute, for teaching
both basic and advanced mechanics.  It has for the most part been implemented
as an addition to Maple, however versions have also been produced to work in
other CAS.  The constructs used in Sophia are designed to have pedagogical
significance and when useful, an infix structure similar to that used in
working with paper and pencil.  Details, such as change of frames, are done
automatically.  The advanced version allows use of modern algorithms, such as
Kane's equations, for treating multibody nonholonomic systems with complex
constraints.  In this lecture the main features of Sophia and examples of how
they are used in basic mechanics education will be demonstrated.  Only slight
reference will be made to more advanced applications.  The software and
tutorial information is also available at the web site
http://www.mech.kth.se/~mlesser

Reference:
M. Lesser
The Analysis of Complex Nonlinear Mechanical Systems, a computer algebra based
approach. World Scientific Press.