{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T04:39:05Z","timestamp":1775018345915,"version":"3.50.1"},"reference-count":20,"publisher":"Pleiades Publishing Ltd","issue":"5","license":[{"start":{"date-parts":[[2023,10,1]],"date-time":"2023-10-01T00:00:00Z","timestamp":1696118400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,10,1]],"date-time":"2023-10-01T00:00:00Z","timestamp":1696118400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Program Comput Soft"],"published-print":{"date-parts":[[2023,10]]},"DOI":"10.1134\/s0361768823020135","type":"journal-article","created":{"date-parts":[[2023,10,9]],"date-time":"2023-10-09T04:55:24Z","timestamp":1696827324000},"page":"433-440","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Resonances and Periodic Motions of Atwood\u2019s Machine with Two Oscillating Weights"],"prefix":"10.1134","volume":"49","author":[{"given":"A. N.","family":"Prokopenya","sequence":"first","affiliation":[]}],"member":"137","published-online":{"date-parts":[[2023,10,9]]},"reference":[{"key":"3757_CR1","volume-title":"A Treatise on the Rectilinear Motion and Rotation of Bodies","author":"G. Atwood","year":"1784","unstructured":"Atwood, G., A Treatise on the Rectilinear Motion and Rotation of Bodies, Cambridge University Press, 1784."},{"key":"3757_CR2","doi-asserted-by":"publisher","first-page":"895","DOI":"10.1119\/1.13791","volume":"52","author":"N.B. Tufillaro","year":"1984","unstructured":"Tufillaro, N.B., Abbott, T.A., and Griffiths, D.J., Swinging Atwood\u2019s machine, Am. J. Phys., 1984, vol.\u00a052, no. 10, pp. 895\u2013903.","journal-title":"Am. J. Phys."},{"key":"3757_CR3","doi-asserted-by":"publisher","first-page":"1495","DOI":"10.1051\/jphys:019850046090149500","volume":"46","author":"N.B. Tufillaro","year":"1985","unstructured":"Tufillaro, N.B., Motions of a swinging Atwood\u2019s machine, J. Phys., 1985, vol. 46, pp. 1495\u20131500.","journal-title":"J. Phys."},{"key":"3757_CR4","doi-asserted-by":"publisher","first-page":"142","DOI":"10.1119\/1.14710","volume":"54","author":"N.B. Tufillaro","year":"1986","unstructured":"Tufillaro, N.B., Integrable motion of a swinging Atwood\u2019s machine, Amer. J. Phys., 1986, vol. 54,  pp. 142\u2013143.","journal-title":"Amer. J. Phys."},{"key":"3757_CR5","doi-asserted-by":"publisher","first-page":"1693","DOI":"10.1051\/jphys:0199000510160169300","volume":"51","author":"J. Casasayas","year":"1990","unstructured":"Casasayas, J., Nunes, T.A., and Tufillaro, N.B., Swinging Atwood\u2019s machine: integrability and dynamics, J. Phys., 1990, vol. 51, pp. 1693\u20131702.","journal-title":"J. Phys."},{"key":"3757_CR6","doi-asserted-by":"publisher","first-page":"711","DOI":"10.1016\/j.mechrescom.2005.06.015","volume":"33","author":"H.M. Yehia","year":"2006","unstructured":"Yehia, H.M., On the integrability of the motion of a heavy particle on a tilted cone and the swinging Atwood\u2019s machine, Mech. R. Comm., 2006, vol. 33, no. 5, pp. 711\u2013716.","journal-title":"Mech. R. Comm."},{"key":"3757_CR7","doi-asserted-by":"publisher","first-page":"1067","DOI":"10.1016\/j.physd.2010.02.017","volume":"239","author":"O. Pujol","year":"2010","unstructured":"Pujol, O., P\u00e9rez, J.P., Ramis, J.P., Simo, C., Simon, S., and Weil, J.A., Swinging Atwood machine: Experimental and numerical results, and a theoretical study, Physica D, 2010, vol. 239, no. 12, pp. 1067\u20131081.","journal-title":"Physica D"},{"key":"3757_CR8","first-page":"417","volume":"11","author":"A.N. Prokopenya","year":"2017","unstructured":"Prokopenya, A.N., Motion of a swinging Atwood\u2019s machine: simulation and analysis with Mathematica, Math. \n               Comput. Sci., 2017, vol. 11, nos. 3\u20134, pp. 417\u2013425.","journal-title":"Comput. Sci."},{"key":"3757_CR9","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1134\/S0361768820020085","volume":"46","author":"A.N. Prokopenya","year":"2020","unstructured":"Prokopenya, A.N., Construction of a periodic solution to the equations of motion of generalized Atwood\u2019s machine using computer algebra, Program. Comput. Software, 2020, vol. 46, no. 2, pp. 120\u2013125.","journal-title":"Program. Comput. Software"},{"key":"3757_CR10","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/s11786-018-0357-1","volume":"13","author":"A.N. Prokopenya","year":"2019","unstructured":"Prokopenya, A.N., Modelling Atwood\u2019s machine with three degrees of freedom, Math. Comput. Sci., 2019, vol.\u00a013, nos. 1\u20132, pp. 247\u2013257.","journal-title":"Math. Comput. Sci."},{"key":"3757_CR11","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1134\/S0361768821010084","volume":"47","author":"A.N. Prokopenya","year":"2021","unstructured":"Prokopenya, A.N., Searching for equilibrium states of Atwood\u2019s machine with two oscillating bodies by means of computer algebra, Program. Comput. Software, 2021, vol. 47, no. 1, pp. 43\u201349.","journal-title":"Program. Comput. Software"},{"key":"3757_CR12","unstructured":"Abramov, S.A., Zima, E.B, and Rostovtsev, V.A., Computer algebra, Programmirovanie, 1992, no. 5, pp.\u00a04\u201325."},{"key":"3757_CR13","unstructured":"Vasil\u2019ev, N.N and Edneral, V.F., Computer algebra in physical and mathematical applications, Programmirovanie, 1994, no. 1, pp. 70\u201382."},{"key":"3757_CR14","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1134\/S0361768806020034","volume":"32","author":"A.N. Prokopenya","year":"2006","unstructured":"Prokopenya, A.N., Some symbolic computation algorithms in cosmic dynamics problem, Program. Comput. Software, 2006, vol. 32, no. 2, pp. 71\u201376.","journal-title":"Program. Comput. Software"},{"key":"3757_CR15","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1134\/S0361768807020028","volume":"33","author":"A.N. Prokopenya","year":"2007","unstructured":"Prokopenya, A.N., Symbolic computation in studying stability of solutions of linear differential equations with periodic coefficients Program. Comput. Software, 2007, vol. 33, no. 2, pp. 60\u201366.","journal-title":"Program. Comput. Software"},{"key":"3757_CR16","doi-asserted-by":"publisher","first-page":"156","DOI":"10.1134\/S0361768812030048","volume":"38","author":"A.N. Prokopenya","year":"2012","unstructured":"Prokopenya, A.N., Hamiltonian normalization in the restricted many-body problem by computer algebra methods, Program. Comput. Software, 2012, vol. 38, no.\u00a03, pp. 156\u2013169.","journal-title":"Program. Comput. Software"},{"key":"3757_CR17","volume-title":"An elementary introduction to the Wolfram Language","author":"S. Wolfram","year":"2017","unstructured":"Wolfram, S., An elementary introduction to the Wolfram Language, Champaign, IL: Wolfram Media, 2017, 2nd ed."},{"key":"3757_CR18","unstructured":"L. D. Landau and E. M. Lifshitz, Mechanics (Nauka, Moscow, 1988; Pergamon, New York, 1976)."},{"key":"3757_CR19","unstructured":"Markeev, A.P., Teoreticheskaya mekhanika (Theoretical Mechanics), Izhevsk: Nauchno-Issled. Tsentr \u201cRegulyarnya i Khaoticheskaya Dinamika\u201d, 2001 [in Russian]."},{"key":"3757_CR20","volume-title":"Introduction to Perturbation Techniques","author":"A.H. Nayfeh","year":"1981","unstructured":"Nayfeh, A.H., Introduction to Perturbation Techniques, New York: Wiley, 1981."}],"container-title":["Programming and Computer Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0361768823020135.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1134\/S0361768823020135","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0361768823020135.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T02:51:55Z","timestamp":1775011915000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1134\/S0361768823020135"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10]]},"references-count":20,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2023,10]]}},"alternative-id":["3757"],"URL":"https:\/\/doi.org\/10.1134\/s0361768823020135","relation":{},"ISSN":["0361-7688","1608-3261"],"issn-type":[{"value":"0361-7688","type":"print"},{"value":"1608-3261","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10]]},"assertion":[{"value":"3 August 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 October 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 October 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 October 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The author declares that he has no conflicts of interest.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"CONFLICT OF INTEREST"}}]}}