% ***********
% * slide_y *
% ***********
% basic rod method
% inputs : lef,height,m,xe,dxe,d2xe,ye,dye,d2ye
%          I,II: m=1; III,IV: m=-1;
% outputs: fi,dfi,d2fi,xf,dxf,d2xf,yf,dyf,d2yf

function [fi,dfi,d2fi,xf,dxf,d2xf,yf,dyf,d2yf]...
    = slide_y(lef,height,m,xe,dxe,d2xe,ye,dye,d2ye)

if xe+lef<height|xe-lef>height
   fi=nan;
   dfi=nan;
   d2fi=nan;
   xf=nan;
   dxf=nan;
   d2xf=nan;
   yf=nan;
   dyf=nan;
   d2yf=nan; 
   return
end

fi=acos((height-xe)/lef);
if m==-1
    fi=-fi;
end
xf=height;
yf=ye+lef*sin(fi);

dfi=dxe/lef/sin(fi);
dxf=0;
dyf=dye+dfi*lef*cos(fi);

d2fi=(d2xe-dfi^2*lef*cos(fi))/lef/sin(fi);
d2xf=0;
d2yf=d2ye+d2fi*lef*cos(fi)-dfi^2*lef*sin(fi);