Mathematical modelling and activation – a study on a large class, a project-based task and students' flow
International audience; We studied how engineering students in a large class (n=346) can be activated by a project-based task, in which they have to model mathematically the motion of an object. The students had to throw an object, use (1) their smart phones for filming, and (2) tracker software for capturing the motion. Through a poster, they had to report their video analysis. We framed activation through the concept of flow, which is a state of being fully absorbed by an activity. We administered a web-based questionnaire (response rate 69%). The results show that such a project-based task is feasible with >300 students and activated them: three out of five experienced flow. Also, we val…
Extended two-body problem for rotating rigid bodies
A new technique that utilizes surface integrals to find the force, torque and potential energy between two non-spherical, rigid bodies is presented. The method is relatively fast, and allows us to solve the full rigid two-body problem for pairs of spheroids and ellipsoids with 12 degrees of freedom. We demonstrate the method with two dimensionless test scenarios, one where tumbling motion develops, and one where the motion of the bodies resemble spinning tops. We also test the method on the asteroid binary (66391) 1999 KW4, where both components are modelled either as spheroids or ellipsoids. The two different shape models have negligible effects on the eccentricity and semi-major axis, but…
Students' usage patterns of video recorded lectures in an undergraduate mathematics course
International audience; It is customary for some universities to offer recordings of live lectures to students. Whether this improves learning and academic performance is debated in the literature. As with most technology, correct usage can lead to increased academic performance, but there are also usage patterns that can be considered counter productive, especially for learning mathematics. In order to investigate patterns in students' usage of such online recorded live lectures, we analyze log files from a server holding the recordings of an undergraduate mathematics course. This poster presents results from the statistical analysis and discusses some of the usage patterns found in light …
Dynamics of asteroid systems post-rotational fission
Asteroid binaries found amongst the Near-Earth objects are believed to have formed from rotational fission. In this paper, we aim to study the dynamical evolution of asteroid systems the moment after fission. The initial condition is modelled as a contact binary, similar to that of Boldrin et al. (2016). Both bodies are modelled as ellipsoids, and the secondary is given an initial rotation angle about its body-fixed $y$-axis. Moreover, we consider six different cases, three where the density of the secondary varies, and three where we vary its shape. The simulations consider 45 different initial tilt angles of the secondary, each with 37 different mass ratios. We start the dynamical simulat…
The planar two-body problem for spheroids and disks
We outline a new method suggested by Conway (2016) for solving the two-body problem for solid bodies of spheroidal or ellipsoidal shape. The method is based on integrating the gravitational potential of one body over the surface of the other body. When the gravitational potential can be analytically expressed (as for spheroids or ellipsoids), the gravitational force and mutual gravitational potential can be formulated as a surface integral instead of a volume integral, and solved numerically. If the two bodies are infinitely thin disks, the surface integral has an analytical solution. The method is exact as the force and mutual potential appear in closed-form expressions, and does not invol…