Continuous versus discrete time dynamical models of Newton's second fundamental law
| العنوان: | Continuous versus discrete time dynamical models of Newton's second fundamental law |
|---|---|
| المؤلفون: | Sergio Invernizzi |
| المصدر: | International Journal of Mathematical Education in Science and Technology. 28:357-365 |
| بيانات النشر: | Informa UK Limited, 1997. |
| سنة النشر: | 1997 |
| مصطلحات موضوعية: | Mathematics (miscellaneous), Discrete time and continuous time, Applied Mathematics, Ordinary differential equation, Mathematical analysis, Zero (complex analysis), Motion (geometry), Initial value problem, Tangent, Function (mathematics), Arc length, Education, Mathematics |
| الوصف: | There exist vertical plane C 1 ‐smooth curves such that the classical Newton mechanics based on ordinary differential equations cannot uniquely determine the future motion of a particle sliding down under the effect of gravity. As a simple example, we explicitly construct a C 1 concave curve 7 such that the tangent component of the gravity as a function of the arc length parameter is F(s)= |s|1/3 sgn (s). Actually, the Cauchy problem ? = F(s), s(0) = 0, ?(0) = 0 has an infinite number of solutions (Peano phenomenon). Physically, this analysis is paradoxical, since it allows that the particle rests motionless at the top of 7 for an arbitrary time interval, and then suddenly moves away. Here we propose a possible solution of the paradox showing that these ‘unwelcome’ solutions are obtained by a limiting process from special orbits of the corresponding discrete time model (which obviously respects the wished determinism in the future) as the fundamental time period ?tgoes to zero. |
| تدمد: | 1464-5211 0020-739X |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_________::e43634ae18daf02847bf70e2230d552a https://doi.org/10.1080/0020739970280305 |
| رقم الأكسشن: | edsair.doi...........e43634ae18daf02847bf70e2230d552a |
| قاعدة البيانات: | OpenAIRE |
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