QuinticPoly.m

classdef QuinticPoly
    % solve the quinticPoly 5th order equation
    
    properties
     % coefficients (c0, c1, c2, c3, c4, c5)
     c
    end
    
    methods (Access = public)
    
        function obj = QuinticPoly (xi0, dxi0, ddxi0, xiT, dxiT, ddxiT, T)
            
           c012= [xi0; dxi0; ddxi0 / 2.0];
           
           M1=[1, T,  T*T;
                   0, 1, 2*T;
                   0, 0,     2 ];
               
            M2=[     T^3,        T^4,        T^5;
                     3*T^2,    4*T^3,    5*T^4;
                         6*T,  12*T^2,  20*T^3 ]; 
                     
             c345 = M2\([xiT; dxiT; ddxiT] - M1 * c012);
             obj.c = [c012; c345];
        end
        
        function x=X(obj, t)
            x=obj.c(1) + obj.c(2).*t + obj.c(3).*t.^2 + obj.c(4).*t.^3 + obj.c(5).*t.^4 + obj.c(6).*t.^5;
        end
        
        function x=dX(obj, t)
            x=obj.c(2) + 2*obj.c(3).*t + 3*obj.c(4).*t.^2 + 4*obj.c(5).*t.^3 + 5* obj.c(6).*t.^4;
        end

        function x=ddX(obj, t)
            x= 2*obj.c(3) + 6*obj.c(4).*t + 12*obj.c(5).*t.^2 + 20* obj.c(6).*t.^3;
        end
        
        
          function x=dddX(obj, t)
            x=  2 + 6*obj.c(4) + 24*obj.c(5).*t + 60* obj.c(6).*t.^2;
        end  
        
       
    end
end