\( \DeclareMathOperator{\abs}{abs} \newcommand{\ensuremath}[1]{\mbox{$#1$}} \)
artificial ramp
(%i1) | e1 : jc + ma· d = j0 + m1· d ; |
determine j1
(%i2) | e2 : j1 = jc + ma· d + m2·( 1 − d) ; |
solve for j1 and d
(%i3) | s1 : linsolve([ e1, e2],[ j1, d]) ; |
(%i4) | ej1 : s1[ 1] ; |
find the steady state j0, labeled J0
(%i5) | e3 : ev( ej1, j1 = j0) ; |
(%i6) | s2 : linsolve( e3, j0) ; |
(%i7) | J0 : rhs( s2[ 1]) ; |
introduce perturbations
(%i8) | e4 : ev( ej1, j1 = J0 + dj1, j0 = J0 + dj0) ; |
solve for dj1
(%i9) | e4 : ratsimp( e4) ; |
(%i10) | fr : solve( e4, dj1) ; |
(%i11) | dj1 : rhs( fr[ 1]) ; |
(%i12) | ratio : dj1 / dj0 ; |
final result
(%i13) | ratio : ratsimp( ratio) ; |
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determine d