Application of a Large-Parameter Technique for Solving a Singular Case of a Rigid Body

Abstract

In this paper, the motion of a rigid body in a singular case of the natural frequency (ω=1/3) is considered. This case of singularity appears in the previous works due to the existence of the term ω2−1/9 in the denominator of the obtained solutions. For this reason, we solve the problem from the beginning. We assume that the body rotates about its fixed point in a Newtonian force field and construct the equations of the motion for this case when ω=1/3. We use a new procedure for solving this problem from the beginning using a large parameter ε that depends on a sufficiently small angular velocity component ro. Applying this procedure, we derive the periodic solutions of the problem and investigate the geometric interpretation of motion. The obtained analytical solutions graphically are presented using programmed data. Using the fourth-order Runge-Kutta method, we find the numerical solutions for this case aimed at determining the errors between both obtained solutions.