Mylar Balloon and Associated Geometro-Mechanical Moments

Vasyl Kovalchuk (), Vladimir I. Pulov and Ivaïlo M. Mladenov
Additional contact information
Vasyl Kovalchuk: Institute of Fundamental Technological Research, Polish Academy of Sciences, 5B, Pawińskiego Str., 02-106 Warsaw, Poland
Vladimir I. Pulov: Department of Mathematics and Physics, Technical University of Varna, Studentska Str. 1, 9010 Varna, Bulgaria
Ivaïlo M. Mladenov: Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Tsarigradsko Chaussee 72, 1784 Sofia, Bulgaria

Mathematics, 2023, vol. 11, issue 12, 1-13

Abstract: Starting with identifications of the very fundamental geometric characteristics of a Mylar balloon such as the profile curve, height, volume, arclength, surface area, crimping factor, etc., using the geometrical moments I n ( x ) and I n , we present explicit formulas for them and those of the mechanical moments of both solid and hollow balloons of arbitrary order. This is achieved by relying on the recursive relationships among elliptic integrals and the final results are expressed via the fundamental mathematical constants such as π , lemniscate constant ω ˜ , and Gauss’s constant G . An interesting periodicity modulo 4 was detected and accounted for in the final formulas for the moments. The principal results are illustrated by two tables, a few graphics, and some direct relationships with other fundamental areas in mathematics, physics and geometry are pointed out.

Keywords: solid and hollow Mylar balloons; crimping factor; geometro-mechanical moments; recursive relations; elliptic integrals and functions; gamma functions; Gauss’s and lemniscate constants (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/12/2646/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/12/2646/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:12:p:2646-:d:1167982

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().