MathModDB:Free Fall Model (Vacuum): Difference between revisions
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As a pedagogical example, let us consider the famous story of [https://portal.mardi4nfdi.de/wiki/Item:Q1437751 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 [[Item:Q3826|Research Field]] named "[[Item:Q3825|Pomology]]" (science of fruits) [[Property:P824|containing]] [[Item:Q3782|"Gravitational Effects on Fruit"]] as a specific [[Item:Q3781|Research Problem]]. Currently, there is a choice of two [[Item:Q3830|Mathematical Models]] addressing this problem, i. e., "Free Fall Models" [[Item:Q3785|without]] and [[Item:Q3784|with]] the effect of air drag, both of them assuming constant gravitation. [[Item:Q3785|The former one]], actually dating back to Newton, contains the simple "[[Item:Q3794|Free Fall Equation]]", | As a pedagogical example, let us consider the famous story of [https://portal.mardi4nfdi.de/wiki/Item:Q1437751 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 is a constant item --> | |||
[[Item:Q3826|Research Field]] | |||
named "[[Item:Q3825|Pomology]]" (science of fruits) [[Property:P824|containing]] [[Item:Q3782|"Gravitational Effects on Fruit"]] as a specific | |||
<!-- Research Problem is a constant item --> | |||
[[Item:Q3781|Research Problem]]. | |||
Currently, there is a choice of two [[Item:Q3830|Mathematical Models]] addressing this problem, i. e., "Free Fall Models" [[Item:Q3785|without]] and [[Item:Q3784|with]] the effect of air drag, both of them assuming constant gravitation. [[Item:Q3785|The former one]], actually dating back to Newton, contains the simple "[[Item:Q3794|Free Fall Equation]]", | |||
<math>v=v_0-gt</math>, as a Mathematical Formulation. That equation contains the free fall velocity <math>v</math>, the gravitational acceleration <math>g</math>, and the time <math>t</math>. Obviously, the first and second of these Quantities are assigned to the [[Item:Q3845|Quantity Kind]] velocity and [[Item:Q3849|acceleration]], respectively. Within the context of these "Free Fall Models", several different Computational Tasks can be formulated, e.g., [[Item:Q3864|how long does it take for an apple to reach the ground]], or [[Item:Q3870|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. | <math>v=v_0-gt</math>, as a Mathematical Formulation. That equation contains the free fall velocity <math>v</math>, the gravitational acceleration <math>g</math>, and the time <math>t</math>. Obviously, the first and second of these Quantities are assigned to the [[Item:Q3845|Quantity Kind]] velocity and [[Item:Q3849|acceleration]], respectively. Within the context of these "Free Fall Models", several different Computational Tasks can be formulated, e.g., [[Item:Q3864|how long does it take for an apple to reach the ground]], or [[Item:Q3870|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. | ||
{{DISPLAYTITLE:{{#invoke:Wd|label}}}} | |||
== Available identifiers == | |||
{{#if: {{#invoke:Wd|label|raw|}} | {{Template:Badge|[[Help:MaRDI QID|MaRDI QID]]|https://portal.mardi4nfdi.de/wiki/Item:{{#invoke:Wd|label|raw|}}|{{#invoke:Wd|label|raw|}}}} }} | |||
== Testing SPARQL with staging portal == | == Testing SPARQL with staging portal == | ||
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{{#sparql: | {{#sparql: | ||
SELECT ?Model | SELECT ?Model | ||
# where Q3782 refers to the Gravitational Effects on Fruit | # where Q3782 refers to the Gravitational Effects on Fruit | ||
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BIND(CONCAT("<a href=", STR(?URL), ">", STR(?Label) ,"</a>") as ?Model) | BIND(CONCAT("<a href=", STR(?URL), ">", STR(?Label) ,"</a>") as ?Model) | ||
} | } | ||
| chart=bordercloud.visualization.DataTable | | chart=bordercloud.visualization.DataTable | ||
| log=2 | | log=2 | ||
}} | }} | ||
Latest revision as of 14:16, 22 November 2024
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", , as a Mathematical Formulation. That equation contains the free fall velocity , the gravitational acceleration , and the time . 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.
Available identifiers
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
