In this paperwe have considered an integro-differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields. This equation contains variable coefficients with large expressions which complicate the application of any numerical method. We have used variational iteration method to find its numerical solution by developing MATHEMATICA modulae and solved a number of numerical examples. The results show high accuracy and efficiency ofour approach.

With the existing kinematic configuration of a humanoid robot, fast turning is the main issue encountered. The joint orientation of the lower body of a humanoid robot does not allow the system to move fast. The first joint of the existing setup is started with the rotary joint vertically up z-direction. A change in the joint orientation had been proposed for the kinematic configuration of the humanoid robot. The first joint in this proposed work is the revolute joint along the x-direction of movement. Forward and inverse kinematics were obtained for the maximum value of the reach of the leg in the environment. Jacobian was described for every joint. Singularity posture was obtained at the location.

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In this paper, a modified iteration method (MIM) has been proposed to solve nonlinear second-order ODEs. Convergence analysis and error estimate of the proposed method are also discussed. Computational efficiency of this method is illustrated through numerical examples.