Mechanical engineering, mechanical engineering technology, and related educational programs are not addressing in a sufficient way the principles associated with applying analytical investigations in solving actual engineering problems. Because of this, graduates do not have the adequate skills required to use the methods of applied dynamics in the process of analyzing mechanical systems. These methods allow one to obtain an understanding of the role of the parameters of a system and to carry out a purposeful control of the values of these parameters with the goal to achieve the desired performance. Engineering and engineering technology programs pay very little attention to addressing these steps. It should be stressed that these programs do not offer a universal straightforward methodology of solving linear differential equations of motion that allow revealing all important interrelationships between the aspects of the engineering problem.
It is difficult to formulate the reasons why there is such a low interest in applying the analytical approach in order to reveal the interrelationships between decisive aspects of the operational process of an engineering system in order to achieve the desired goal. Actually, there is almost a complete silence with regard to this issue. Hence, we assume that the first reason could be that there is no recognition of the existence of such a problem. In other words, there is no need to apply these analytical methods since these methods are not beneficial. We do not believe that the engineering community supports this reason. It is not a matter of demonstrating factual data that show how many times the theory was helpful. Without the support of the theory we cannot justifiably evaluate the results of our solutions. If we agree that there is problem, then why are there no publications that would stimulate discussions leading toward a solution of the problem?
Here is the second reason. Until now, engineering programs do not present the straightforward universal theoretically sound methodologies for solving the second order linear differential equations that are vital for mechanical and electrical engineering. Without any suggestions of how to solve this problem, it did not make much sense to begin a discussion. In our opinion, this is why we have silence with the regard to this problem.
However, it is well known that Laplace Transforms allow solving any linear differential equation of motion. It is justifiable to assume that the main reason why the Laplace Transform methodology is not adopted by learning environments consists in the absence of the majority of tables of Laplace Transform Pairs that are needed for solving differential equations of motion as well as differential equations describing electrical circuits. However, the situation is changed. Current publications comprise the adequate tables that are needed for solving linear differential equations of motion associated with all common mechanical engineering problems.
Practicing engineers and students need assistance in acquiring the knowledge of composing differential equations of motion. They need certain training in solving these equations using Laplace Transform methodology. Several recommendations are proposed on how to expedite the implementation in academia and in industry of the methods of applied dynamics in solving common mechanical engineering problems.
Laplace transform and Hyers–Ulam stability of linear differential equations
