Abstract:

The achievement of a comprehensive education of the students to provide a global knowledge that allows them to make appropriate decisions in the framework of their future work is one of the most important challenges of the Engineering degrees, especially in basic subjects as Physics or Mathematics. In this sense, a great effort has to be done by the teachers of the first year where the subjects are generally quite abstract and, as a consequence, the motivation of the students are hard to attain. Several are the conditions to obtain this goal successfully: First, a correct cross-coordination and a well-designed teaching of the basis subjects to avoid undesirable repetition of some concepts under different point of view and to show the basic knowledge as a uniform conceptual body ready to be applied to real situations. Second, the need to make attractive the study of these basic and abstract subjects by proposing the resolution of real problems related with the goals of each particular Degree, and adapted to the knowledge of the student of the first level. These problems have to be solved involving different branch of the basic subjects as Physics or Mathematics.

In this paper we present a real project related to the professional skills of the Geomatic and Topography Degree, adapted for the first level, and involving three core subjects namely, Algebra, Calculus and Mechanics. The approach of this real project, proposed as an interdisciplinary practice, is related with the path followed by a rocket that puts a satellite in orbit. In real situations, sixteen are the steps of the protocol to achieve this goal, from the takeoff of the rocket to its entrance on the final elliptic orbit.

To adapt this complicated protocol to our purposes, we have simplified the steps considering finally only four:
(i) the takeoff of the rocket;
(ii) the change of the upright path at a predetermined height from the ground to approach to the elliptical orbit;
(iii) the link between the rise of the rocket and its placing in elliptical orbit; (iv) the putting into the elliptical orbit itself.

Analysis of classic geometric figures as the conics, with their different forms of representation, becomes necessary to be able to develop this practice, since they adapt to the forms described by orbits of the satellites. Modeling makes it necessary to use different reference systems and their relationship between them. In addition, the simplified study of the satellite position vector in its different phases provides fundamental data such as speed, acceleration or balance of forces, related with the subjects of Dynamic or Kinematics, and where the concept of derivative plays a fundamental role. A later detailed study on the movement of the satellite would lead to propose systems of differential equations that relate the elements studied and whose complexity requires numerical methods for their resolution.

References:
[1] Sánchez-Pérez, J.V., Balaguer-Beser, A., Checa-Martínez, E., Marín-Molina, J., Ferri, M., Bravo, J.M. (2015). Multidisciplinary practices for first engineering level: obtaining the gravitational acceleration experimentally. Proceedings of EDULEARN15 conference, pp. 656-664, Barcelona, Spain.
[2] R.Kent Nagle et al. Ecuaciones diferenciales y problemas con valores en la frontera. 4ª edición. Pearson Educación ,2015, ISBN 970-26-0592-X

Keywords:

Multidisciplinary learning, Theoretical-experimental learning.