alpha_0 = 2.607703208923340e-08           % seconds
alpha_1 = 7.450580596923828e-09           % seconds per semi-circle
alpha_2 = -1.192092895507813e-07          % seconds per square semi-circle
alpha_3 = 0           % seconds per cubic semi-circle

beta_0 = 129024                         % seconds
beta_1 = 0                           	% seconds per semi-circle
beta_2 = -262144                        % seconds per square semi-circle
beta_3 = 131072                         % seconds per cubic semi-circle