Spherical Pedal Coordinates and Calculus of Variations

D 2024

Spherical Pedal Coordinates and Calculus of Variations

BLASCHKE, Petr

Základní údaje

Originální název

Spherical Pedal Coordinates and Calculus of Variations

Autoři

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

Vydání

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

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 XL, WGMP 2022

Kód RIV

RIV/47813059:19610/24:A0000153

Organizační jednotka

Matematický ústav v Opavě

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

Klíčová slova anglicky

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

Štítky

MÚ, RIV25

Příznaky

Mezinárodní význam, Recenzováno

Návaznosti

GA21-27941S, projekt VaV.

Změněno: 5. 3. 2025 14:19, Mgr. Aleš Ryšavý

Anotace

V originále

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.

Citovat

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, s. 209-221. ISBN 978-3-031-62406-3. Dostupné z: 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, s.~209-221. ISBN~978-3-031-62406-3. Dostupné z: https://doi.org/10.1007/978-3-031-62407-0\_{}16.

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