In the ruminant production from meadows or pastures, close relationships among fields, forages and ruminants are of great importance to the cycling of nutrient elements (Whitehead, 2000a, b), because this will lead to sustainable systems of ruminant production from forages (Mannetje, 1994; Peel and Lloveras, 1994; Spedding, 1995). Our previous report (Shimojo et al., 2002) suggested an example of analytic description of field-forage-ruminant relationships by introducing a concept of an intersection of forage production and ruminant production, where animals were related to fields through forages eaten and feces excreted. There will be other analytic ways that might be expected to give symbolic descriptions of these relationships. We tried to apply the complex representation to analytic studies of digestibility or indigestibility changes with growth of forages (Shimojo et al., 1998a, b). In some cases of scientific studies, the complex representation of a subject might be helpful to its understanding when described using polar coordinates and subjected to rotations on the complex plane.
The present study was designed to give a symbolic representation of field-forage -ruminant relationships using rotations on the complex plane of polar coordinates describing digestible and indigestible dry matter of forages connected with fields.