Talk:SICM

Untitled

I'm removing these paragraphs; they look like they're copied without attribution from something else. (The use of the second-person pronouns suggests a book jacket or similar.) jdb ❋ 15:58, 30 Dec 2004 (UTC)

Traditional courses in mechanics concentrate most of their efforts on the extremely small class of algebraically tractable dynamical systems. Such subjects are biased toward a few simple examples that can be deeply analyzed with rather magnificent amounts of mathematical machinery.

But most systems cannot be solved by purely symbolic methods, however powerful. In general, we should not expect problems to yield to algebra. But even when a system is not completely solvable, the tools of modern dynamics allow one to extract a qualitative understanding. Rather than concentrating on the symbolic description of particular trajectories, SICM concentrates on geometric features of the set of possible trajectories. Such tools provide a basis for the systematic analysis of numerical or experimental data.

However, this must be done in a natural way, weaving these techniques into the powerful theoretical structure of classical theory.