Consistent Order Approximations in Extended Thermodynamics of Polyatomic Gases

In this article the known models are considered for relativistic polyatomic gases with an arbitrary number of moments, in the framework of Extended Thermodynamics. These models have the downside of being hyperbolic only in a narrow domain around equilibrium, called "hyperbolicity zone". Here it is shown how to overcome this drawback by presenting a new model which satisfies the hyperbolicity requirement for every value of the independent variables and without restrictions. The basic idea behind this new model is that hyperbolicity is limited in previous models by the approximations made there. It is here shown that hyperbolicity isn't limited also for an approximated model if terms of the same order are consistently considered, in a new way never used before in literature. To design and complete this new model, well accepted principles are used such as the "Entropy Principle" and the "Maximum Entropy Principle". Finally, new trends are analized and these considerations may require a modification of the results published so far; as a bonus, more manageable balance equations are obtained. This allows to obtain more stringent results than those so far known. For example, we will have a single quantity (the energy e) expressed by an integral and all the other constitutive functions will be expressed in terms of it and its derivatives with respect to temperature. Another useful consequence is its easier applicability to the case of diatomic and ultrarelativistic gases which are useful, at least for testing the model in simple cases.