Simulacija gibanja zvrka pomoću programskog jezika Python

master's thesis

• Title (english): Spinning top simulations using the Python
• Author: Jasnik Ivanjek
• Mentor: Tamara Nikšić (mentor)
• Committee member: Mirko Planinić (predsjednik povjerenstva)
• Committee member: Katarina Jeličić (član povjerenstva)
• Committee member: Matko Milin (član povjerenstva)
• Committee member: Tamara Nikšić (član povjerenstva)
• Committee member: Maja Planinić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2019-02-18, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

U ovom radu razmatramo ulogu računalnih simulacija kao nadopunu ili alternativu izvođenju pokusa u nastavi fizike. Postupak izrade računalne simulacije ilustriran je na primjeru zvrka. Jednadžbe gibanja zvrka postavljene su u sustavu zvrka (Eulerove jednadžbe) što vodi na sustav običnih vezanih diferencijalnih jednadžbi koje najčešće možemo riješiti samo numerički. Pritom smo se, radi jednostavnosti, ograničili na problem zvrka koji rotira oko fiksirane točke, odnosno eliminirali smo mogućnost translacija. Za izradu simulacije koristili smo programski jezik Python 3 i njegove biblioteke numpy i scipy za numeričko rješavanje diferencijalnih jednadžbi te paket VPython za vizualizaciju gibanja zvrka. Izrađene simulacije obuhvaćaju slobodni simetrični i asimetrični zvrk, te simetrični, asimetrični i Kovaleskayin zvrk u polju sile teže. Na primjerima pokazujemo kako oblik zvrka, vanjska sila i početni uvjeti utječu na gibanje zvrka. Ove i slične simulacije mogle bi pomoći u nastavi fizike kada nemamo uvjete za izvođenje pokusa ili izvedeni pokus želimo nadopuniti simulacijom kako bismo učenicima dodatno približili teorijsku pozadinu određenog fizikalnog problema.

Abstract (english)

In this thesis, we consider the role of computer simulations as a supplement or an alternative to performing experiments in teaching physics. The computer simulation process is illustrated by the example of the spinning top. The spinning top equations of motion are derived in the moving system attached to the top (Euler’s equations) leading to a system of coupled ordinary differential equations that one usually solves numerically. For simplicity, we restrict the problem to rotation around the fixed point thus eliminating the translational degrees of freedom. In order to solve the Euler’s equations, we used the Python 3 programming language together with numpy and scipy packages. Spinning top visualization is performed with VPython. Simulations include free symmetric and asymmetric top, as well as the heavy symmetric, asymmetric and Kovaleskaya top. We illustrate the influence of the shape of the spinning top, the external force and the initial conditions on the motion of the top. These and similar simulations could be useful in teaching physics when we cannot perform the experiment or when the teacher wants to use the simulation as the supplement to the experiment in order to further explain the theoretical background of a particular physical problem.

• Keywords: simulacija; zvrk; Python; Eulerove jednadžbe; kruto tijelo
• Keywords (english): simulation; spinning top; Python; Euler's equations; rigid body
• Language: croatian
• URN:NBN: urn:nbn:hr:217:284478
• Study programme: Title: Physics and Computer Science; specializations in: Education; Course: Education; Study programme type: university; Study level: integrated undergraduate and graduate; Academic / professional title: magistar/magistra fizike i informatike (magistar/magistra fizike i informatike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-04-17 10:38:15