Kanonične transformacije

delo diplomskega seminarja

Alan Krumenaker (Author), George Mejak (Mentor)

Abstract

Kanonične transformacije so pomembno orodje v klasični mehaniki, saj omogočajo poenostavitev številnih mehanskih problemov. V delu najprej predstavimo osnovne koncepte Lagrangeeve in Hamiltonove mehanike ter opišemo enačbe, ki določajo gibanje mehanskih sistemov. Osrednja pozornost je namenjena kanoničnim transformacijam, ki olajšajo reševanje gibalnih enačb. Podrobno obravnavamo rodovne funkcije in njihovo povezavo s kanoničnimi transformacijami ter preučimo matematične lastnosti kanoničnih transformacij. Poudarek je tudi na uporabi teh transformacij pri konkretnih problemih. Na koncu obravnavamo še Poissonove oklepaje in kanonične invariante.

Keywords

enačbe gibanja;mehanski sistemi;Lagrangeeva funkcija;Hamiltonova funkcija;Poissonov oklepaj;kanonična transformacija;harmonično nihalo;

Data

Language:	Slovenian
Year of publishing:	2024
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[A. Krumenaker]
UDC:	531/533
COBISS:	208502787
Views:	40
Downloads:	9
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Canonical transformations
Secondary abstract:	Canonical transformations are an important tool in classical mechanics, as they simplify the solution of many mechanical problems. This work first introduces the basic concepts of Lagrangian and Hamiltonian mechanics and describes the equations governing the motion of mechanical systems. The main focus is on canonical transformations, which facilitate the solving of equations of motion. We thoroughly examine generating functions and their connection to canonical transformations, as well as the mathematical properties of canonical transformations. Emphasis is also placed on the application of these transformations to specific problems. Finally, we explore Poisson brackets and canonical invariants.
Secondary keywords:	equations of motion;mechanical systems;Lagrangian;Hamiltonian;Poisson bracket;canonical transformation;harmonic oscillator;
Type (COBISS):	Final seminar paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	40 str.
ID:	25105165