1transfor.mac is from the book "Perturbation Methods, Bifurcation 2Theory and Computer Algebra" by Rand & Armbruster (Springer 1987) 3 4The procedure transform() performs an arbitrary (not necessarily 5linear) coordinate transformation on a system of differential 6equations. 7 8The example is from p43. maxima-5.9.0 cvs reproduces the 9results from the book. 10 11(C1) load("./transfor.mac"); 12(D1) ./transfor.mac 13(C2) transform(); 14ENTER NUMBER OF EQUATIONS 153; 16ENTER SYMBOL FOR ORIGINAL VARIABLE 1 17x; 18ENTER SYMBOL FOR ORIGINAL VARIABLE 2 19y; 20ENTER SYMBOL FOR ORIGINAL VARIABLE 3 21z; 22ENTER SYMBOL FOR TRANSFORMED VARIABLE 1 23u; 24ENTER SYMBOL FOR TRANSFORMED VARIABLE 2 25v; 26ENTER SYMBOL FOR TRANSFORMED VARIABLE 3 27w; 28THE RHS'S OF THE D.E.'S ARE FUNCTIONS OF THE ORIGINAL VARIABLES: 29ENTER RHS OF x D.E. 30D x /DT = 31s*(y-x); 32D x /DT = s (y - x) 33ENTER RHS OF y D.E. 34D y /DT = 35r*x-y-x*z; 36D y /DT = - x z - y + r x 37ENTER RHS OF z D.E. 38D z /DT = 39-b*z+x*y; 40D z /DT = x y - b z 41THE TRANSFORMATION IS ENTERED NEXT: 42ENTER x AS A FUNCTION OF THE NEW VARIABLES 43x = 44u+v; 45x = v + u 46ENTER y AS A FUNCTION OF THE NEW VARIABLES 47y = 48u-v/s; 49 v 50y = u - - 51 s 52ENTER z AS A FUNCTION OF THE NEW VARIABLES 53z = 54w; 55z = w 56 du s (u w + (1 - r) u) + s v (w - r + 1) 57(D2) [[-- = - -------------------------------------, 58 dT s + 1 59 60 2 61dv s ((r - 1) u - u w) + v (s (- w + r + 1) + s + 1) 62-- = - --------------------------------------------------, 63dT s + 1 64 65 2 2 66dw s (b w - u ) + v + (u - s u) v 67-- = - -------------------------------]] 68dT s 69 70Local Variables: *** 71mode: Text *** 72End: ***