Pedal Coordinates and Orbits Inside Magnetic Dipole Field

D 2023

Pedal Coordinates and Orbits Inside Magnetic Dipole Field

BLASCHKE, Petr

Basic information

Original name

Pedal Coordinates and Orbits Inside Magnetic Dipole Field

Authors

BLASCHKE, Petr (203 Czech Republic, guarantor, belonging to the institution)

Edition

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

Publisher

Birkhäuser Cham

Other information

Language

English

Type of outcome

Proceedings paper

Field of Study

10101 Pure mathematics

Country of publisher

Switzerland

Confidentiality degree

is not subject to a state or trade secret

Publication form

printed version "print"

References:

Geometric Methods in Physics XXXIX

RIV identification code

RIV/47813059:19610/23:A0000126

Organization unit

Mathematical Institute in Opava

ISBN

978-3-031-30286-2

ISSN

DOI

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

EID Scopus

2-s2.0-85165958551

Keywords in English

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

Links

GA21-27941S, research and development project.

Changed: 27/3/2024 15:00, Mgr. Aleš Ryšavý

Abstract

In the original language

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.

Cite

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, p. 147-158. ISBN 978-3-031-30286-2. Available from: https://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 = {https://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  - CONF
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, p.~147-158. ISBN~978-3-031-30286-2. Available from: https://doi.org/10.1007/978-3-031-30284-8\_{}14.

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