4.5 Newton-Raphson Method for a nonlinear equation Solve position constraint equations For each time step,solve nonlinear equation of the position coordinates by use of Newton-Raphson algorithm Φi+=Φa+Φ，g0Aq0+high-order terms SinceΦi+)≈0 Φ，P4q0=-Φ0 f②，|≠0 Solve equation,4g0--Φ0 If by use of Gaussian method to obtain the position coordinate vector of the next time step as q+)=q0+q0 Until lg-qo<s orFor each time step, solve nonlinear equation of the position coordinates by use of Newton-Raphson algorithm (i) (i) (i) q q   high order terms i i i i     ( 1) ( ) ( ) ( )   q q 0 ( 1)  i Since  Solve equation (i 1) (i) (i) q  q  q  (i) (i) (i) q q   by use of Gaussian method to obtain the position coordinate vector of the next time step as Until If 0 ( )  i q    (i1) (i) q q or   (i)  Solve position constraint equations