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 Research Field named "Pomology" (science of fruits) containing "Gravitational Effects on Fruit" as a specific Research Problem. Currently, there is a choice of two Mathematical Models addressing this problem, i. e., "Free Fall Models" without and with the effect of air drag, both of them assuming constant gravitation. The former one, actually dating back to Newton, contains the simple "Free Fall Equation", $v=v_0-gt$, as a Mathematical Formulation. 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., how long does it take for an apple to reach the ground, or with which velocity will it hit the ground. 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.

List of Related Research Fields

Research Field
Pomology

List of Related Mathematical Models

Mathematical Model
MathModDB: Free Fall Model (Air Drag)

List of Computational Tasks using this Mathematical Model

1. {| class="wikitable" style="margin:auto"
2. |+
3. |-
4. ! Computational Task
5. |-
6. | Free Fall Determine Time
7. |-
8. | Free Fall Determine Velocity
9. |-
10. | Free Fall Determine Gravitation
11. |}

List of Related Literature

Literature
https://doi.org/10.1017/CBO9780511818509