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- #| -*-Scheme-*-
- Copyright (C) 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994,
- 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005,
- 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Massachusetts
- Institute of Technology
- This file is part of MIT/GNU Scheme.
- MIT/GNU Scheme is free software; you can redistribute it and/or modify
- it under the terms of the GNU General Public License as published by
- the Free Software Foundation; either version 2 of the License, or (at
- your option) any later version.
- MIT/GNU Scheme is distributed in the hope that it will be useful, but
- WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
- General Public License for more details.
- You should have received a copy of the GNU General Public License
- along with MIT/GNU Scheme; if not, write to the Free Software
- Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301,
- USA.
- |#
- #|
- ;;; Let (sigma t) be the state of a system at time t. Let the
- ;;; (first-order) system of differential equations governing the
- ;;; evolution of this state be:
- ;;; ((D sigma) t) = (R (sigma t))
- ;;; or (D sigma) = (compose R sigma)
- ;;; i.e. R is a system derivative.
- ;;; Let F be any function of state, then a differential equation for
- ;;; the evolution of F, as it is dragged along the integral curve
- ;;; sigma is:
- ;;; (D (compose F sigma)) = (* (compose (D F) sigma) (D sigma))
- ;;; = (compose (* (D F) R) sigma)
- ;;; Let's call this operation Lie-D (the Lie derivative for
- ;;; coordinates). We define
- |#
- (define (Lie-D R)
- (define (the-LD F) (* (D F) R))
- (make-operator the-LD `(Lie-D ,R)))
-
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