... at the contact points of rolling elements and races, whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The numerical integration technique Newmark-β with the Newton–Raphson method is used to solve the nonlinear differential equations, iteratively. The effect of bearing running...

... couplings differential algebraic equations kinematics Newton-Raphson method railways vehicle dynamics longitudinal train forces coupler geometric nonlinearities noninertial coordinates railroad vehicle dynamics multibody systems Coupler elements that connect train cars have...

... accommodated. The direct integration beta- m method in conjunction with the Newton–Raphson method is seen to work extremely well for the nonlinear analysis. The linear transient response analysis only requires beta- m method. Fast Fourier transforms are also performed to find quantitatively...