MathModDB:Free Fall Model (Vacuum)

As a pedagogical example, let us consider the famous story of Sir Isaac Newton being inspired to formulate his theory of gravitation by watching the fall of an apple from a tree in the year 1666. We have implemented this within the MathModDB knowledge graph by including a academic discipline named "pomology" (science of fruits) containing "Gravitational Effects on Fruit" as a specific research problem. Currently, there is a choice of three mathematical models addressing this problem, i. e., "Free Fall Models". The first two assume constant gravitation without and with the effect of air drag whereas the third one neglects the aerodynamic drag (vanishing drag coefficient and/or density of air) but does also account for a non-uniform gravitational field. The first one, actually dating back to Newton, contains the simple "Free Fall Equation", $v (t) = v_{0} - g t$ , as a mathematical expression. That equation contains the free fall velocity $v$ , the Gravitational Acceleration $g$ , and the time $t$ . Obviously, the first and second of these Quantities are assigned to the Quantity Kind velocity and Acceleration, respectively. Within the context of these "Free Fall Models", several different Computational Tasks can be formulated, e.g.,

While the above equation (without air drag) is so simple that it can be solved analytically, in more realistic free fall models the underlying equations have to be solved numerically which falls into the realm of the MathAlgoDB knowledge graph containing suitable numerical solvers for ordinary differential equations such as the Runge Kutta family of algorithms. Finally, we mention that also more complex models involving gravitational effects have been implemented in MathModDB, such as the dynamics of planets in our solar system.

Testing SPARQL with staging portal

Get a list of models that are used for the research problem Gravitational Effects on Fruit

Get how many models are used for the research problem Gravitational Effects on Fruit

Testing SPARQL with Münster Infrastructure

List of Formulations

List of Related Research Fields

List of Computational Tasks using this Mathematical Model

Testing SPARQL with wikidata