Spherical Pedal Coordinates and Calculus of Variations

D 2024

Spherical Pedal Coordinates and Calculus of Variations

BLASCHKE, Petr

Basic information

Original name

Spherical Pedal Coordinates and Calculus of Variations

Authors

BLASCHKE, Petr

Edition

978-3-031-62406-3. Cham, Switzerland, Geometric Methods in Physics XL, Trends in Mathematics, p. 209-221, 13 pp. 2024

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 XL, WGMP 2022

RIV identification code

RIV/47813059:19610/24:A0000153

Organization unit

Mathematical Institute in Opava

ISBN

978-3-031-62406-3

ISSN

DOI

https://doi.org/10.1007/978-3-031-62407-0_16

UT WoS

001308717200016

EID Scopus

2-s2.0-85202583497

Keywords in English

Calculus of variation; Classical mechanics; Pedal coordinates; Spherical pedal coordinates

Links

GA21-27941S, research and development project.

Changed: 5/3/2025 14:19, Mgr. Aleš Ryšavý

Abstract

In the original language

Planar curves can be described in terms of pedal coordinates. We will introduce a generalization of this notion for curves on a sphere in Euclidean space. It is observed that certain problems in the calculus of variations can be solved with the help of these coordinates [1]. In particular, we show how the notion of spherical pedal coordinates can be used to solve the spherical version of isoperimetric problems and the problem of brachistochrone.

Cite

BLASCHKE, Petr. Spherical Pedal Coordinates and Calculus of Variations. In Piotr Kielanowski, Daniel Beltita, Alina Dobrogowska, Tomasz Goliński. Geometric Methods in Physics XL, Trends in Mathematics. 978-3-031-62406-3. Cham, Switzerland: Birkhäuser Cham, 2024, p. 209-221. ISBN 978-3-031-62406-3. Available from: https://doi.org/10.1007/978-3-031-62407-0_16.

@inproceedings{82970,
   author = {Blaschke, Petr},
   address = {Cham, Switzerland},
   booktitle = {Geometric Methods in Physics XL, Trends in Mathematics},
   doi = {https://doi.org/10.1007/978-3-031-62407-0_16},
   edition = {978-3-031-62406-3},
   editor = {Piotr Kielanowski, Daniel Beltita, Alina Dobrogowska, Tomasz Goliński},
   keywords = {Calculus of variation; Classical mechanics; Pedal coordinates; Spherical pedal coordinates},
   howpublished = {tištěná verze "print"},
   language = {eng},
   location = {Cham, Switzerland},
   isbn = {978-3-031-62406-3},
   pages = {209-221},
   publisher = {Birkhäuser Cham},
   title = {Spherical Pedal Coordinates and Calculus of Variations},
   url = {https://link.springer.com/chapter/10.1007/978-3-031-62407-0_16},
   year = {2024}
}

TY  - CONF
ID  - 82970
AU  - Blaschke, Petr
PY  - 2024
TI  - Spherical Pedal Coordinates and Calculus of Variations
PB  - Birkhäuser Cham
CY  - Cham, Switzerland
SN  - 9783031624063
KW  - Calculus of variation
KW  - Classical mechanics
KW  - Pedal coordinates
KW  - Spherical pedal coordinates
UR  - https://link.springer.com/chapter/10.1007/978-3-031-62407-0_16
N2  - Planar curves can be described in terms of pedal coordinates. We will introduce a generalization of this notion for curves on a sphere in Euclidean space. It is observed that certain problems in the calculus of variations can be solved with the help of these coordinates [1]. In particular, we show how the notion of spherical pedal coordinates can be used to solve the spherical version of isoperimetric problems and the problem of brachistochrone.
ER  -

BLASCHKE, Petr. Spherical Pedal Coordinates and Calculus of Variations. In Piotr Kielanowski, Daniel Beltita, Alina Dobrogowska, Tomasz Goli\'nski. \textit{Geometric Methods in Physics XL, Trends in Mathematics}. 978-3-031-62406-3. Cham, Switzerland: Birkhäuser Cham, 2024, p.~209-221. ISBN~978-3-031-62406-3. Available from: https://doi.org/10.1007/978-3-031-62407-0\_{}16.

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