Repository of Department of Physics in Osijek
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LAGRANGE POINTS AS SPACECRAFT PARKING SPOTS
No full textLagrangeove točke označuju položaje u sustavu dvaju masivnih tijela gdje treće tijelo, znatno manje mase, može ostati u ravnoteži u korotirajućem referentnom sustavu. U uvodnom dijelu ovog rada daje se pregled važnosti i povijesti proučavanja ovih točaka, s naglaskom na konkretne svemirske misije na L-točke sustava Sunce-Zemlja. Nadalje je dan teorijski i matematički opis Lagrangeovih točaka, uključujući i analizu njihove stabilnosti. Dana je simulacija, implementirana u programskom jeziku Python, koja određuje svih pet Lagrangeovih točaka za različite planetarne sustave, računajući efektivni potencijal u korotirajućem referentnom sustavu. Cilj rada je pružiti sveobuhvatan uvid u fizikalne i matematičke osnove ovih točaka te istaknuti njihovu važnost u suvremenoj astrodinamici.Lagrange points represent positions in a system of two massive bodies where a third body, of significantly smaller mass, can remain in equilibrium within a co-rotating reference frame. The introductory section of this thesis provides an overview of the importance and historical context of studying these points, with particular emphasis on specific space missions to the L-points of the Sun-Earth system. A theoretical and mathematical description of the Lagrange points is then presented, including an analysis of their stability. A simulation implemented in the Python programming language is provided, which determines all five Lagrange points for various planetary systems by computing the effective potential in the corotating reference frame. The aim of this thesis is to offer a comprehensive insight into the physical and mathematical foundations of these points and to highlight their significance in contemporary astrodynamics
COMPARISON OF DIFFERENT MOTION CAPTURE TECHNIQUES ON CHARACTERISTIC EXAMPLES IN KINEMATICS AND THEIR APPLICATION IN PHYSICS EDUCATION
No full textKarakteristična gibanja (jednoliko i jednoliko ubrzano pravocrtno gibanje, slobodni pad kao njegov poseban slučaj i harmonijsko titranje) koja se pojavljuju u kurikulumu nastave Fizike snimljena su i analizirana različitim eksperimentalnim tehnikama (elektromagnetsko tipkalo, Tracker, akcelerometar mobitela i Cobra4). Dobiveni rezultati su prikazani tablično i grafički.
Provedena statistička analiza je pokazala da među bilo koja dva para izmjerenih i/ili izračunatih vrijednosti ubrzanja odnosno ubrzanja sile teže u bilo kojoj kombinaciji primijenjenih tehnika snimanja gibanja nije utvrđena statistički signifikantna razlika. S obzirom na uočene prednosti i nedostatke ovih tehnika snimanja gibanja preporučena je njihova primjena u nastavi fizike.Characteristic motions (uniform and uniformly accelerated linear motion, free fall as its special case, and harmonic oscillation) that appear in the Physics curriculum were recorded and analyzed using various experimental techniques (electromagnetic tracking system, Tracker, mobile phone accelerometer, and Cobra4). The obtained results are presented in tables and
graphs. The statistical analysis performed showed that no statistically significant difference was found between any two pairs of measured and/or calculated acceleration values including free fall acceleration, in any combination of applied motion recording techniques. According to observed advantages and disadvantages of these motion recording techniques, their application in physics teaching is recommended
STUDY OF STABILITY OF ANTIMONENE STRUCTURES WITH DEFECTS
No full textAntimonen je dvodimenzionalni materijal čija se jedinstvena elektronska, mehanička i optička svojstva još uvijek istražuju. U ovom radu istražena je svijena struktura antimonena sa šupljinama s ciljem razumijevanja kako prisutnost šupljina utječe na stabilnost i elektronska svojstva materijala. Analizirano je 30 struktura antimonena s različitim vrstama i kombinacijama šupljina. Sve strukture su proučavane putem simulacija temeljenih na teoriji funkcionala gustoće (DFT), implementiranim u Quantum Espresso paket. Ovaj rad omogućava uvid u potencijalne primjene struktura antimonena s defektima u modernim tehnologijama.Antimony is two-dimensional material whose unique electronic, mechanical and optical properties are still being explored. In this thesis, the stability of the antimonene structures with defects was investigated with the aim of understanding how the presence of vacancies affect the stability and electronic properties of the material. 30 different antimonene structures with different types and combinations of vacancies were used for the analysis. All structures were studied by simulation based on density functional theory (DFT), implemented in the Quantum Espresso package. This thesis provides insight into the potential applications of the defective structure of antimonene in modern technologies
Physical Astrognosy: Modern Celestial Cartography
No full textPojas astronomskog zodijaka sastoji se od 13 zviježđa (ne 12 kao astrološki) i ona nisu sva jednako velika (za razliku od astroloških). Osim toga, astronomija ima još 75 dodatnih zviježđa na cijelom nebeskom svodu sjeverne i južne hemisfere. U ovome radu će se pokazati i objasniti što su uopće zviježđa, kako i zašto su astronomi podijelili nebo na ukupno 88 područja te zašto je danas važna fizička astrognozija odnosno poznavanje položaja i nazivlja zviježđa. U praktičnom dijelu rada, napravljena je aplikacija u Pythonu koja koristi bazu podataka svih zviježđa s hrvatskim, engleskim i latinskim nazivima, te koordinatama "centra mase" dijela površine neba koji obuhvaća pojedino zviježđe. Za bilo koji unešeni naziv zviježđa (hrvatski, engleski ili latinski) program daje sva tri naziva i nebeske koordinate odabranog središta zviježđa te na karti (preuzetoj sa [12]) ucrtava točku s tim koordinatama.The astronomical zodiac consists of 13 constellations (not 12 as astrological) and they are not all the same size (unlike astrological). In addition, astronomy has 75 additional constellations throughout the northern and southern hemispheres. In this paper, we will explain what the constellations are, how and why astronomers divided the sky into a total of 88 areas, and why physical astrognosia, i.e. knowledge of the positions and names of the constellations, is important today. In the practical part of the work, an application was created in Python that uses a database of all constellations with Croatian, English
and Latin names, as well as the coordinates of the "center of mass" of the part of the sky surface that includes each constellation. For any entered constellation name (Croatian, English or Latin), the program gives all three names and the celestial coordinates of the selected constellation center and draws a point with these coordinates on the map (downloaded from [12])
KLASIFIKACIJA AKTIVNIH GALAKTICKIH JEZGRI
No full textIn this Bachelor’s Thesis, active galactic nuclei (AGN), their properties, as well as different classification schemes are presented. The first part explains what active galactic nuclei are. The second part explains their properties and the physical mechanisms necessary for their understanding at the undergraduate level. The thesis also provides a historical overview of the classification of active galactic nuclei as well as the two most famous classification attempts: Fanaroff-Riley classification and Unified schemes based on orientation. Finally, multiwavelength light curves are shown as well as the spectral energy distribution of a spesific active galactic nucleus, the blazar S4 0954+65.U ovom završnom radu predstavljene su aktivne galaktičke jezgre, njihova svojstva, kao i različite klasifikacijske sheme. Prvi dio, objašnjava što su aktivne galaktičke jezgre. Drugi dio objašnjava njihova svojstva i fizikalne mehanizme potrebne za njihovo razumijevanje na pred- diplomskoj razini. U radu je dan i povijesni pregled klasifikacije aktivnih galaktičkih jezgara kao i dva najpoznatija pokušaja klasifikacije: Fanaroff-Riley klasifikacija i unificirane sheme temeljene na orijentaciji. Na kraju su prikazani viševalne svjetlosne krivulje kao i spektralna raspodjela energije jedne aktivne galaktičke jezgre, blazara S4 0954+65
Application for calculating parameters of black hole from its mass and spin
No full textCrne rupe fascinantni su astronomski objekti koje nastaju prilikom gravitacijskog urušavanja masivnih zvijezda. Iako konceptualno postoje još od 18. stoljeća (John Mitchell, 1783.), pojam crne rupe kako ju danas razumijemo razvio je Karl Schwarzschild 1916. godine pomoću Einsteinove teorije relativnosti. Godine 1971. konačno je i otkrivena crna rupa Cygnus X-1. Cilj ovog rada je predstaviti pojam crne rupe, od njezinih konceptualnih početaka sve do određenih saznanja koja danas imamo o crnim rupama. Ovaj rad također će prikazati ulogu mase i spina crne rupe u njezinom fizikalnom opisu, te ćemo u konačnici vidjeti kako se određeni parametri crne rupe računaju iz mase i spina pomoću jednostavne aplikacije.Black holes are fascinating astronomical objects created by gravitational collapse of massive stars. Although conceptualized during 18th century (John Mitchell, 1783), concept of black hole as we understand it today was developed by Karl Schwarzschild in 1916 using Einstein’s theory of relativity. In 1971 first black hole was finally discovered and named Cygnus
X-1. Aim of this thesis is to present the concept of a black hole, all the way since its conceptualization to understanding of black holes we have today. This thesis will also show the role of mass and spin in its description of physical properties, and finally we will see how certain parameters are calculated, in regards to its mass and spin, using a simple application
Experiments in magnetism performed using the Sciensation kit
No full textMagnetizam se odnosi na pojave povezane s magnetskim silama i poljima. U radu su prikazani pokusi iz magnetizma i elektromagnetizma, izvedeni pomoću pribora „Sciensation“, koji omogućuje sigurno izvođenje u nastavi. Pokusi su prikladni za osnovnoškolsko i srednjoškolsko obrazovanje, a obuhvaćaju ključne pojmove kao što su električna struja, magnetsko polje, indukcija i sl. Svaki pokus započinje teorijskim uvodom, a zatim slijede zadaci, opažanja, objašnjenja i zaključci, uz pripremljene radne listiće za učenike.Magnetism refers to phenomena associated with magnetic forces and fields. This thesis presents experiments in magnetism and electromagnetism, performed using the "Sciensation" kit, which allows safe execution in classroom settings. The experiments are suitable for primary and secondary school education, covering key concepts such as electric current, magnetic field, induction, and more. Each experiment begins with a theoretical introduction, followed by tasks, observations, explanations, and conclusions, along with prepared worksheets for students
Numerical analysis of the motion of a 1D mathematical pendulum in the limit of small amplitudes
No full textMatematičko (jednostavno) njihalo je titrajni sustav u kojemu je čestica mase obješena na donjem kraju nerastezive niti zanemarive mase duljine . U ovome radu napravljen je računalni program u Pythonu koji numerički računa rješenja diferencijalnih jednadžbi za jednostavno, prigušeno, prisilno i nelinearno matematičko njihalo u granici malih amplituda. Uz pomoć
Eulerove metode i Euler-Cromerove metode dobivena su grafička i numerička rješenja u slučajevima kada osim gravitacijske sile djeluju sila prigušenja i vanjska periodična sila.A mathematical (simple) pendulum is a oscillating system in which a particle of mass is suspended at the lower end of a thread of negligible mass length . In this paper, a computer program in Python was created that numerically calculates the solutions of differential equations for a simple, damp, forced and nonlinear mathematical pendulum in the limit of small
amplitudes. With the help of the Euler method and the Euler-Cromer method, graphical and numerical solutions were obtained in cases where, in addition to the gravitational force, the damping force and the external periodic force act
Numerička analiza i vizualizacija putanja tijela u Sunčevom sustavu
No full textThis thesis presents a numerical analysis and visualization of the trajectories of celestial bodies in the solar system. Utilizing Newton's laws of motion and gravitational force, differential equations governing these motions are solved numerically using Python. Both the Euler-Cromer method and the odeint integrator are employed, with their results graphically represented to illustrate
position. The study verifies the conservation of angular momentum through data on aphelion and perihelion. The odeint function, dynamically adjusts its method for accuracy, while the EulerCromer method ensures stability in long-term simulations. The findings confirm the numerical methods' alignment with classical theories like Kepler's laws, demonstrating the effectiveness of
Python for astrophysical computations and establishing a foundation for future research in celestial mechanics.Ovim zavšrnim radom predstavljamo numeričku analizu i vizualizaciju putanja nebeskih tijela u Sunčevom sustavu. Koristeći Newtonove zakone gibanja i gravitacije, postavljamo diferencijalne jednadžbe koje opisuju ta gibanja te ih rješavamo numerički pomoću Pythona. Koristimo EulerCromerovu metodu i odeint integrator, te njihove rezultate prikazujemo grafički za ilustraciju položaja. Funkcija odeint dinamički prilagođava svoju metodu za točnost, dok Euler-Cromerova metoda osigurava stabilnost u dugoročnim simulacijama. U radu potvrđujemo očuvanje kutne količine kretanja pomoću podataka o afelu i perihelu. Nalazi potvrđuju usklađenost numeričkih metoda s klasičnim teorijama poput Keplerovih zakona, te pokazuju učinkovitost Pythona za astrofizičke proračune i postavljaju temelj za buduća istraživanja nebeske mehanike
2D ALUMINIUM - FUNCTIONALIZATION AND ENCAPSULATION
No full textU ovom radu proučava se oksidacija 2D aluminija (aluminena) krenuvši od teorijskog modela adsorpcije kisika kao metode funkcionalizacije aluminena, zatim stvaranje aluminijevog oksida te na kraju mogućnost zaštite aluminena od oksidacije postupkom enkapsulacije. Istraživanje je provedeno primjenjujući teoriju funkcionala gustoće (eng. density functional theory), skraćeno
DFT. Iz dobivenih rezultata zaključuje se da adsorpcija kisika rezultira novom alotropskom modifikacijom aluminena, dok vezanjem kisika u aluminen nastaje aluminijev oksid. Također, rezultati ukazuju na mogućnost zaštite aluminena od oksidacije enkapsulacijom pomoću grafena.In this work, the oxidation of 2D aluminum (aluminum) is studied, starting from the theoretical model of oxygen adsorption as a method of aluminum functionalization. Then the formation of aluminum oxide is studied, and finally a possible way of protecting aluminum from oxidation by the encapsulation process. The research was carried out using density functional theory (DFT). From the obtained results, it can be concluded that a new allotropic modification of aluminum is formed by the adsorption of oxygen, while aluminum oxide is formed by the binding of oxygen into aluminene. Also, the results indicate the possibility of protecting aluminum from oxidation by encapsulation using graphene