Differences between source and new form of the Euler-Bernoulli equation and its solution

In construction of complex robotic and related mechanisms, lightweight materials are often used and they are characterized by flexibility segments. To achieve precise and rapid control of motion of such a mechanism, it is necessary to synthesize their high fidelity model. This would be of great importance for its analysis and synthesis. The work in this paper starts from the first research in this area, and it includes the original form of the Euler-Bernoulli equation and its solution, which, compared with current knowledge, imposes the need for the expansion of the same equation from multiple points of view. The new form of the Euler-Bernoulli equation and its solution are based on current knowledge in robotics, as well as the knowledge of classical mechanics. This is the only way of how to fully preserve the information of the complexity of the kinematics and dynamics of elastic mechanisms.