The Differential Equations of Gravity-free Double Pendulum: Lauricella Hypergeometric Solutions and Their Inversion
Alessio Bocci, Giovanni Mingari Scarpello
Asian Research Journal of Mathematics · pp. 1–18 · Published 17 Mar 2022
10.9734/arjom/2022/v18i330362Abstract
This paper solves in closed form the system of ODEs ruling the 2D motion of a gravity free double pendulum (GFDP), not subjected to any force. In such a way its movement is governed by the initial conditions only. The relevant strongly non linear ODEs have been put back to hyperelliptic quadratures which, through the Integral Representation Theorem (IRT), are driven to the Lauricella hypergeometric functions. We compute time laws and trajectories of both point masses forming the GFDP in explicit closed form. Suitable sample problems are carried out in order to prove the method effectiveness.
Cited by 1
S. I. Bezrodnykh · Integral transforms and special functions · 2025
Related research
- Some Applications of One and Two- Dimensional Fourier Series and Transforms — shares topic coverage
- Fourier Coefficients of A Class of Eta Quotients of Weight 6 — shares topic coverage
- Delayed Nutrient Conversion for a Single Species Periodic Chemostat — shares topic coverage
- Chemostat Model with Periodic Nutrient Input Described by Fourier Series — shares topic coverage
- Analytic Inversion of Closed form Solutions of the Satellite’s J2 Problem — shares topic coverage
Article metrics
Real usage data collected on this platform.
8
Page views
0
PDF downloads
0
Outbound clicks
1
Citations
Views over time
Views by country
Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".
Traffic sources
Referring site, by host.
Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.