Pedal Coordinates and Orbits Inside Magnetic Dipole Field

D 2023

Pedal Coordinates and Orbits Inside Magnetic Dipole Field

BLASCHKE, Petr

Základní údaje

Originální název

Pedal Coordinates and Orbits Inside Magnetic Dipole Field

Autoři

BLASCHKE, Petr (203 Česká republika, garant, domácí)

Vydání

Cham, Switzerland, Geometric Methods in Physics XXXIX, Trends in Mathematics, od s. 147-158, 12 s. 2023

Nakladatel

Birkhäuser Cham

Další údaje

Jazyk

angličtina

Typ výsledku

Stať ve sborníku

Obor

10101 Pure mathematics

Stát vydavatele

Švýcarsko

Utajení

není předmětem státního či obchodního tajemství

Forma vydání

tištěná verze "print"

Odkazy

Geometric Methods in Physics XXXIX

Kód RIV

RIV/47813059:19610/23:A0000126

Organizační jednotka

Matematický ústav v Opavě

ISBN

978-3-031-30286-2

ISSN

DOI

http://dx.doi.org/10.1007/978-3-031-30284-8_14

Klíčová slova anglicky

Calculus of variation; Classical mechanics; Integrable system; Pedal coordinates; Systems of Frenet–Serret type

Štítky

MÚ

Příznaky

Mezinárodní význam, Recenzováno

Návaznosti

GA21-27941S, projekt VaV.

Změněno: 27. 3. 2024 15:00, Mgr. Aleš Ryšavý

Anotace

V originále

We will compare two different techniques to solve a problem of motion of a charged particle inside magnetic dipole field. One “classical” and the other using pedal coordinates. We will show that even though the classical approach gives an exact solution in terms of known function, pedal coordinates offer much better understanding of the solution and also offer a mean to manipulate the obtained orbits in order to be able to link them with existing curves and other force problems.

Citovat

BLASCHKE, Petr. Pedal Coordinates and Orbits Inside Magnetic Dipole Field. In Piotr Kielanowski, Alina Dobrogowska, Gerald A. Goldin, Tomasz Goliński. Geometric Methods in Physics XXXIX, Trends in Mathematics. Cham, Switzerland: Birkhäuser Cham, 2023, s. 147-158. ISBN 978-3-031-30286-2. Dostupné z: https://dx.doi.org/10.1007/978-3-031-30284-8_14.

@inproceedings{78302,
   author = {Blaschke, Petr},
   address = {Cham, Switzerland},
   booktitle = {Geometric Methods in Physics XXXIX, Trends in Mathematics},
   doi = {http://dx.doi.org/10.1007/978-3-031-30284-8_14},
   editor = {Piotr Kielanowski, Alina Dobrogowska, Gerald A. Goldin, Tomasz Goliński},
   keywords = {Calculus of variation; Classical mechanics; Integrable system; Pedal coordinates; Systems of Frenet–Serret type},
   howpublished = {tištěná verze "print"},
   language = {eng},
   location = {Cham, Switzerland},
   isbn = {978-3-031-30286-2},
   pages = {147-158},
   publisher = {Birkhäuser Cham},
   title = {Pedal Coordinates and Orbits Inside Magnetic Dipole Field},
   url = {https://link.springer.com/chapter/10.1007/978-3-031-30284-8_14},
   year = {2023}
}

TY  - JOUR
ID  - 78302
AU  - Blaschke, Petr
PY  - 2023
TI  - Pedal Coordinates and Orbits Inside Magnetic Dipole Field
PB  - Birkhäuser Cham
CY  - Cham, Switzerland
SN  - 9783031302862
KW  - Calculus of variation
KW  - Classical mechanics
KW  - Integrable system
KW  - Pedal coordinates
KW  - Systems of Frenet–Serret type
UR  - https://link.springer.com/chapter/10.1007/978-3-031-30284-8_14
N2  - We will compare two different techniques to solve a problem of motion of a charged particle inside magnetic dipole field. One “classical” and the other using pedal coordinates. We will show that even though the classical approach gives an exact solution in terms of known function, pedal coordinates offer much better understanding of the solution and also offer a mean to manipulate the obtained orbits in order to be able to link them with existing curves and other force problems.
ER  -

BLASCHKE, Petr. Pedal Coordinates and Orbits Inside Magnetic Dipole Field. In Piotr Kielanowski, Alina Dobrogowska, Gerald A. Goldin, Tomasz Goli\'nski. \textit{Geometric Methods in Physics XXXIX, Trends in Mathematics}. Cham, Switzerland: Birkhäuser Cham, 2023, s.~147-158. ISBN~978-3-031-30286-2. Dostupné z: https://dx.doi.org/10.1007/978-3-031-30284-8\_{}14.

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