Trajectories of a ball moving inside a spherical cavity using first integrals of the governing nonlinear system
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68378297%3A_____%2F21%3A00546147" target="_blank" >RIV/68378297:_____/21:00546147 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s11071-021-06709-4" target="_blank" >https://doi.org/10.1007/s11071-021-06709-4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11071-021-06709-4" target="_blank" >10.1007/s11071-021-06709-4</a>
Alternative languages
Result language
angličtina
Original language name
Trajectories of a ball moving inside a spherical cavity using first integrals of the governing nonlinear system
Original language description
Analytical study of ball vibration absorber behavior is presented in the paper. The dynamics of trajectories of a heavy ball moving without slipping inside a spherical cavity are analyzed. Following our previous work, where a similar system was investigated through various numerical simulations, research of the dynamic properties of a sphere moving in a spherical cavity was carried out by methods of analytical dynamics. The strategy of analytical investigation enabled definition of a set of special and limit cases which designate individual domains of regular trajectories. In order to avoid any mutual interaction between the domains along a particular trajectory movement, energy dissipation at the contact of the ball and the cavity has been ignored, as has any kinematic excitation due to cavity movement. A governing system was derived using the Lagrangian formalism and complemented by appropriate non-holonomic constraints of the Pfaff type. The three first integrals are defined, enabling the evaluation of trajectory types with respect to system parameters, the initial amount of total energy, the angular momentum of the ball and its initial spin velocity. The neighborhoods of the limit trajectories and their dynamic stability are assessed. Limit and transition special cases are investigated along with their individual elements. The analytical means of investigation enabled the performance of broad parametric studies. Good agreement was found when comparing the results achieved by the analytical procedures in this paper with those obtained by means of numerical simulations, as they followed from the Lagrangian approach and the Appell–Gibbs function presented in previous papers.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
20101 - Civil engineering
Result continuities
Project
<a href="/en/project/GA19-21817S" target="_blank" >GA19-21817S: Nonholonomic interaction and dynamical stability of aeroelastic systems</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Nonlinear Dynamics
ISSN
0924-090X
e-ISSN
1573-269X
Volume of the periodical
106
Issue of the periodical within the volume
3
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
35
Pages from-to
1591-1625
UT code for WoS article
000700201100003
EID of the result in the Scopus database
2-s2.0-85115435662