Parabolic Sandwiches for Functions on a Compact Interval and an Application to Projectile Motion
About a century ago, the French artillery commandant Charbonnier envisioned an intriguing result on the trajectory of a projectile that is moving under the forces of gravity and air resistance. In 2000, Groetsch discovered a significant gap in Charbonnier’s work and provided a valid argument for a c...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2019/4868106 |
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| _version_ | 1832563328011993088 |
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| author | Robert Kantrowitz Michael M. Neumann |
| author_facet | Robert Kantrowitz Michael M. Neumann |
| author_sort | Robert Kantrowitz |
| collection | DOAJ |
| description | About a century ago, the French artillery commandant Charbonnier envisioned an intriguing result on the trajectory of a projectile that is moving under the forces of gravity and air resistance. In 2000, Groetsch discovered a significant gap in Charbonnier’s work and provided a valid argument for a certain special case. The goal of the present article is to establish a rigorous new approach to the full result. For this, we develop a theory of those functions which can be sandwiched, in a natural way, by a pair of quadratic polynomials. It turns out that the convexity or concavity of the derivative plays a decisive role in this context. |
| format | Article |
| id | doaj-art-f3f2a918d0524223b96c360d80ffdcf8 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f3f2a918d0524223b96c360d80ffdcf82025-02-03T01:20:27ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252019-01-01201910.1155/2019/48681064868106Parabolic Sandwiches for Functions on a Compact Interval and an Application to Projectile MotionRobert Kantrowitz0Michael M. Neumann1Mathematics Department, Hamilton College, 198 College Hill Road, Clinton, NY 13323, USADepartment of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USAAbout a century ago, the French artillery commandant Charbonnier envisioned an intriguing result on the trajectory of a projectile that is moving under the forces of gravity and air resistance. In 2000, Groetsch discovered a significant gap in Charbonnier’s work and provided a valid argument for a certain special case. The goal of the present article is to establish a rigorous new approach to the full result. For this, we develop a theory of those functions which can be sandwiched, in a natural way, by a pair of quadratic polynomials. It turns out that the convexity or concavity of the derivative plays a decisive role in this context.http://dx.doi.org/10.1155/2019/4868106 |
| spellingShingle | Robert Kantrowitz Michael M. Neumann Parabolic Sandwiches for Functions on a Compact Interval and an Application to Projectile Motion International Journal of Mathematics and Mathematical Sciences |
| title | Parabolic Sandwiches for Functions on a Compact Interval and an Application to Projectile Motion |
| title_full | Parabolic Sandwiches for Functions on a Compact Interval and an Application to Projectile Motion |
| title_fullStr | Parabolic Sandwiches for Functions on a Compact Interval and an Application to Projectile Motion |
| title_full_unstemmed | Parabolic Sandwiches for Functions on a Compact Interval and an Application to Projectile Motion |
| title_short | Parabolic Sandwiches for Functions on a Compact Interval and an Application to Projectile Motion |
| title_sort | parabolic sandwiches for functions on a compact interval and an application to projectile motion |
| url | http://dx.doi.org/10.1155/2019/4868106 |
| work_keys_str_mv | AT robertkantrowitz parabolicsandwichesforfunctionsonacompactintervalandanapplicationtoprojectilemotion AT michaelmneumann parabolicsandwichesforfunctionsonacompactintervalandanapplicationtoprojectilemotion |