Open AccessAscending Disk: Theoretical and Numerical Study
Author(s) -
Rodolfo da Silva Espíndola,
Gabriela del Valle,
Gerardo Hernández,
Inti Pineda,
D. Muciño,
P. Díaz,
S. Guijosa
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1221/1/012051
Subject(s) - rotation formalisms in three dimensions , extension (predicate logic) , phase space , classical mechanics , runge–kutta methods , principal part , plane (geometry) , principal (computer security) , physics , mathematics , newtonian fluid , work (physics) , mathematical analysis , numerical analysis , computer science , geometry , thermodynamics , programming language , operating system
In this work we analyzed a classical mechanical problem: a disc with a circular hole rotating and ascending on a inclined plane. The principal idea is to show the basic equations in both Lagrangian and Newtonian formalisms and to present numerical solutions. The equations are not solvable analytically, then we proceed to integrate numerically using the standardized Runge-Kutta method of order 4. We present several phase space showing the time evolution of the system. Additionally we presented an extension of the system considering a damping factor that decays exponentially in time.