/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created with wxMaxima version 21.11.0 ] */
/* [wxMaxima: input   start ] */
/*
With the parameters a_ref and T² and the function f with derivatives and inverses, the formulas are:
*/
s_max = a_ref * T²;
t = T * f_inv(s / s_max);
s(t,T) := s_max * f(t/T);
v(s,T) := s_max / T * (1 / f_inv_1(s / s_max));
p(s,T) := T / s_max * f_inv_1(s / s_max);
a(t,T) := a_ref * f_2(t/T);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
/*
It is important, that f_inv_1(x) can be calculated stable for x<<<1 over several decades well.

Due to this a segmental definition could be useful.
For example x³ and cubic root can be calculated easily for several decades close to 0.
*/
a:0.5 $
b:1.46 $
select(x) := x < a $
seg1(x) :=1.295* x^3 $
seg2(x) := 1-(1-seg1(a))*sin((1-x)*%pi/b)/sin((1-a)*%pi/b) $
seg1_1(x):=diff(seg1(x),x)$
seg2_1(x):=diff(seg2(x),x)$
seg1_2(x):=diff(seg1(x),x,2)$
seg2_2(x):=diff(seg2(x),x,2)$
f(x) := if select(x) then seg1(x) else seg2(x) $
[seg1_1(x),seg2_1(x)];wxplot2d([f(x),%[1],%[2]],[x,0,1]);
/* [wxMaxima: input   end   ] */


/* [wxMaxima: input   start ] */
[seg1_2(x),seg2_2(x)];wxplot2d([%[1],%[2]],[x,0,1]);
/* [wxMaxima: input   end   ] */



/* Old versions of Maxima abort on loading files that end in a comment. */
"Created with wxMaxima 21.11.0"$