def laplace_and_matrix(): t, s = symbols('t, s') if False: y = laplace(exp(t), t, s) disp(y) y = laplace(4+5*exp(-3*t), t, s) disp(y) y = laplace(4+5*exp(-3*t), t, s) disp(y) disp( laplace(2*t-3*exp(-t), t, s) ) # poly p = poly( [9, 1], s ) q = poly( [3, 7, 1], s ) f = p/q disp( f ) # final/init value # Не всегда применими, см. видеолекции Classical Control Theory by # Brian Douglas # # https://en.wikipedia.org/wiki/Final_value_theorem final_val = limit( s*f, s, 0 ) disp( final_val ) initial_val = limit( s*f, s, inf ) disp( initial_val ) f = (s+3)/((s+1)*(s+2)*(s+4)) A = pfss(f) map( lambda v: disp( ilaplace(v, s, t) ), A )
def main(): # laplace print laplace(exp(-t), t, s)