“…where T refers to kinetic energy, V refers to potential energy, U i refers to the velocity of the node, and F i refers to the external force applied to the node. The expression for the total kinetic energy of the beam unit 21,22 is where _ u xo , _ u yo , and _ u zo , refer to translation velocity on X, Y, and Z, respectively, in m/s; u x , u y , and u z refer to the angles of the beam element section around the xaxes, y-axes, and z-axes, respectively, in rad; _ u x , _ u y , and _ u z refer to the angular speed of the beam element section around the x-axes, y-axes, and z-axes, in rad/s; e refers to the eccentric distance of a section, in m; O refers to the actual rotation speed of drill string in the pit, rad/s; r refers to the density of drill string, in kg/m 3 ; l e refers to the length of a beam element, in m; A refers to the cross-sectional area of a beam element, in m 2 ; I x refers to the polar moment of inertia of the cross section of a beam element, in m 4 ; I yz refers to the moment of inertia of the cross section of a beam element, in m 4 . In equation ( 3), the first three terms represent the translational kinetic energy, while the last two terms represent the rotational kinetic energy.…”