This paper is the second of two companion papers addressing the dynamics of two coupled masses sliding on analytical surfaces and interacting with one another. The motion occurs under the effect of gravity, the reaction force of the surface and basal friction. The interaction force maintains the masses at a fixed distance and lies on the line connecting them. The equations of motion form a system of ordinary differential equations that are solved through a fourth-order Runge–Kutta numerical scheme. In the first paper we considered an approximate method holding when the line joining the masses is almost tangent to the surface at the instant mass positions. In this second paper we provide a general solution. Firstly, we present special cases in which the system has exact solutions. Second, we consider a series of numerical examples where the interest is focused on the trajectories of the masses and on the intensity and changes of the interaction force.

Numerical solutions for point masses sliding over analytical surfaces: Part 2

Tinti, Stefano;Gallotti, Glauco
2019

Abstract

This paper is the second of two companion papers addressing the dynamics of two coupled masses sliding on analytical surfaces and interacting with one another. The motion occurs under the effect of gravity, the reaction force of the surface and basal friction. The interaction force maintains the masses at a fixed distance and lies on the line connecting them. The equations of motion form a system of ordinary differential equations that are solved through a fourth-order Runge–Kutta numerical scheme. In the first paper we considered an approximate method holding when the line joining the masses is almost tangent to the surface at the instant mass positions. In this second paper we provide a general solution. Firstly, we present special cases in which the system has exact solutions. Second, we consider a series of numerical examples where the interest is focused on the trajectories of the masses and on the intensity and changes of the interaction force.
File in questo prodotto:
File Dimensione Formato  
11585_724573.pdf

accesso aperto

Tipo: Versione (PDF) editoriale
Licenza: Licenza per Accesso Aperto. Creative Commons Attribuzione - Non commerciale - Non opere derivate (CCBYNCND)
Dimensione 3.8 MB
Formato Adobe PDF
3.8 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/724573
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact