Applications of the Lie symmetries to complete solution of a bead on a rotating wire hoop

The existence of Lie symmetries in differential equations can generate transformations in the dependent and independent variables and obtain new equations that may be easier to integrate. In particular, in some situations, one can reduce the order and it is possible to obtain first integrals. Thus,...

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Bibliographic Details
Published in:Journal of the Brazilian Society of Mechanical Sciences and Engineering 2018-02, Vol.40 (2), p.1-6, Article 48
Main Authors: Basquerotto, Cláudio H. C. Costa, Righetto, Edison, Silva, Samuel da
Format: Article
Language:English
Subjects:
Dependent variables
Differential equations
Elliptic functions
Engineering
Independent variables
Integrals
Mathematical analysis
Mechanical Engineering
Mechanical systems
Technical Paper
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Summary:The existence of Lie symmetries in differential equations can generate transformations in the dependent and independent variables and obtain new equations that may be easier to integrate. In particular, in some situations, one can reduce the order and it is possible to obtain first integrals. Thus, this article presents the application of the fundamental Lie theorem to obtain the complete solution of a classical nonlinear problem of the dynamics of mechanical systems: the bead on a rotating wire hoop. From the first integral obtained with the Lie symmetry generators, the exact solution can be found with the aid of the Jacobi elliptic functions.
ISSN:1678-5878
1806-3691
DOI:10.1007/s40430-018-0995-x