Theoretical Mathematics & Applications

Lagrange’s equations of motion for oscillating central-force field

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• Abstract

  A body undergoing a rotational motion under the influence of an attractive force may equally oscillate vertically about its own axis of rotation. The up and down vertical oscillation will certainly cause the body to possess another different generalized coordinates in addition to the rotating coordinate. We have shown analytically and qualitatively in this work, the effect of the vertical oscillating motion of a body caused by the vibrational effect of the attractive central force. The total energy possess by the body is now the sum of the radial energy and the oscillating energy. The results show that the total energy is negative and highly attractive.