Geodesic
The~existence proof for forced oscillations by adding dissipative forces in the~example of a~spherical pendulum
Teoretičeskaâ i matematičeskaâ fizika, Tome 211 (2022) no. 2, pp. 295-305

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We consider a generalization of Whitney's problem of periodic motion of an inverted spherical pendulum in the presence of a horizontal periodic force, in addition assuming that velocity-dependent forces act on the pendulum. A method of the introduction of additional dissipative forces is presented. This method allows us to prove the existence of forced oscillations in the considered problem.
Keywords: forced oscillations, Whitney pendulum, stability, periodic solution
Mots-clés : Lorentz force, friction. 
@article{TMF_2022_211_2_a8,
     author = {I. Yu. Polekhin},
     title = {The~existence proof for forced oscillations by adding dissipative forces in the~example of a~spherical pendulum},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {295--305},
     publisher = {mathdoc},
     volume = {211},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2022_211_2_a8/}
}
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I. Yu. Polekhin. The~existence proof for forced oscillations by adding dissipative forces in the~example of a~spherical pendulum. Teoretičeskaâ i matematičeskaâ fizika, Tome 211 (2022) no. 2, pp. 295-305. http://geodesic.mathdoc.fr/item/TMF_2022_211_2_a8/