Dimenzija prostora leg sistema togih teles : delo diplomskega seminarja

Jezeršek, Marija (author), Pavešić, Petar (mentor)

V delu je predstavljen problem dimenzije prostora leg sistema togih teles. Predstavljena je ena od formul za reševanje problema in protiprimer, ki pokaže, da ne deluje v splošnem. Nato je predstavljen sistematičen pristop k reševanju problema, ki temelji na metodah abstraktne algebre. Razvita je teorija kolobarjev polinomov, idealov in raznoterosti, potrebna za obravnavo dimenzije rešitev sistema enačb. Na primerih je prikazana uporaba razvite metode.

• Language: Slovenian
• Keywords: prostor leg, število prostostnih stopenj, kolobar polinomov, ideal, raznoterost, dimenzija raznoterosti, Gröbnerjeva baza, Buchbergerjev algoritem
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2024
• PID: 20.500.12556/RUL-161880
• UDC: 531/533
• COBISS.SI-ID: 208195587
• Publication date in RUL: 15.09.2024

Secondary language

• Language: English
• Title: Mobility of a system of rigid bodies

Abstract

The work presents the problem of the mobility of a system of rigid bodies. We demonstrate one of the common formulas for solving the problem and an example that shows that it does not work in general. Then, a systematic approach based on methods of abstract algebra is established. The main focus is on the theory of polynomial rings, ideals, varieties and their dimension. Two examples are given to illustrate the developed method.

• Keywords: configuration space, degrees of freedom, polynomial ring, ideal, variety, dimension of a variety, Gröbner basis, Buchberger’s algorithm