Abstract
This paper has a didactic aim. The Einstein General Theory of Relativity is very difficult for undergraduates students and also for graduates who have not followed a course of study in gravitational physics. For example, the calculation of some of its known consequences, such as the gravitational time dilation, requires familiarity with space-time metrics. In this paper, starting with the analogy between the electromagnetic field and the inertial one, we want to analyze, through the Einstein Equivalence Principle (EEP), some simple effect in a fictious gravitational field by using the inertial potentials in analogy with the electromagnetic ones.
Highlights
In the classical mechanics, it is well known that for the holonomic systems is valid the following Lagrange equation of motion [1,2,3]d ∂T ∂T dt ∂qi − ∂qi = Qi, (1) where T =T (t, q, q) is the kinetic energy, qi dqi dt are called generalized velocities while Qi are the generalized components of the forces defined by Qi n j=1 Fj · ∂Pj ∂qi (2)
Thanks to Equivalence Principle (EEP), we impose that all inertial potentials can be seen, from the point of view of the accelerated observer, as gravitational potentials
In our opinion, some effects predicted by the relativistic theory of gravitation, can be understood by students by applying the potentials of classical mechanics without knowing the complex mathematical formalism of general relativity
Summary
It is well known that for the holonomic systems is valid the following Lagrange equation of motion [1,2,3]. We review the formal analogy between the electromagnetic field and the field of the inertial accelerations. In this way it is possible to define for the inertial field a generalized potential analogous to the well known one defined, in the electromagnetic framework, by the previous relation (6). Thanks to EEP, we impose that all inertial potentials can be seen, from the point of view of the accelerated observer, as gravitational potentials In this way, in our opinion, some effects predicted by the relativistic theory of gravitation, can be understood by students by applying the potentials of classical mechanics without knowing the complex mathematical formalism of general relativity.
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