Płociniczak, Łukasz; Wróblewska, Zofia Solution and asymptotic analysis of a boundary value problem in the spring-mass model of running. (English) Zbl 1434.34052 Nonlinear Dyn. 99, No. 4, 2693-2705 (2020). MSC: 34E10 34B15 70K60 PDF BibTeX XML Cite \textit{Ł. Płociniczak} and \textit{Z. Wróblewska}, Nonlinear Dyn. 99, No. 4, 2693--2705 (2020; Zbl 1434.34052) Full Text: DOI
Duka, Bejo; Duka, Raimonda On the elastic pendulum, parametric resonance and ’pumping’ swings. (English) Zbl 1421.70038 Eur. J. Phys. 40, No. 2, Article ID 025005, 11 p. (2019). MSC: 70K28 70K75 70K55 97M50 PDF BibTeX XML Cite \textit{B. Duka} and \textit{R. Duka}, Eur. J. Phys. 40, No. 2, Article ID 025005, 11 p. (2019; Zbl 1421.70038) Full Text: DOI
Stronge, W. J. Impact mechanics. 2nd edition. (English) Zbl 1412.74002 Cambridge: Cambridge University Press (ISBN 978-0-521-84188-7/hbk; 978-1-139-05022-7/ebook). xx, 362 p. (2019). MSC: 74-02 74M20 70E18 74M15 70E55 70F35 PDF BibTeX XML Cite \textit{W. J. Stronge}, Impact mechanics. 2nd edition. Cambridge: Cambridge University Press (2019; Zbl 1412.74002) Full Text: DOI
Zubritskiĭ, A. M.; Sokolov, B. M. Energy control of a pendulum with elastic joint. (Russian. English summary) Zbl 1395.70008 Differ. Uravn. Protsessy Upr. 2017, No. 3, 210-216 (2017). MSC: 70E17 93B52 PDF BibTeX XML Cite \textit{A. M. Zubritskiĭ} and \textit{B. M. Sokolov}, Differ. Uravn. Protsessy Upr. 2017, No. 3, 210--216 (2017; Zbl 1395.70008) Full Text: Link
Jurčič-Zlobec, B.; Stanovnik, A. The elastic Foucault pendulum. (English) Zbl 1310.70027 Appl. Math. Comput. Sci. 5, No. 1, 277-285 (2013). MSC: 70K20 37M20 37M05 37N30 PDF BibTeX XML Cite \textit{B. Jurčič-Zlobec} and \textit{A. Stanovnik}, Appl. Math. Comput. Sci. 5, No. 1, 277--285 (2013; Zbl 1310.70027)
Kapitaniak, M.; Perlikowski, P.; Kapitaniak, T. Synchronous motion of two vertically excited planar elastic pendula. (English) Zbl 1311.70014 Commun. Nonlinear Sci. Numer. Simul. 18, No. 8, 2088-2096 (2013). MSC: 70E17 PDF BibTeX XML Cite \textit{M. Kapitaniak} et al., Commun. Nonlinear Sci. Numer. Simul. 18, No. 8, 2088--2096 (2013; Zbl 1311.70014) Full Text: DOI Link
Bastien, Jérôme; Bernardin, Frédéric; Lamarque, Claude-Henri Non-regular deterministic or stochastic discrete dynamical systems. Applications to models with friction or impact. (Systèmes dynamiques discrets non réguliers déterministes ou stochastiques. Applications aux modèles avec frottement ou impact.) (French) Zbl 1270.74002 Collection Mécanique des Structures. Paris: Hermes; Paris: Lavoisier (ISBN 978-2-7462-3908-1/pbk). 532 p. (2012). Reviewer: Petre P. Teodorescu (Bucureşti) MSC: 74-02 74M10 74M20 74S60 37N15 PDF BibTeX XML Cite \textit{J. Bastien} et al., Systèmes dynamiques discrets non réguliers déterministes ou stochastiques. Applications aux modèles avec frottement ou impact. Paris: Hermes; Paris: Lavoisier (2012; Zbl 1270.74002)
Lila, D. M. Stability of the stationary motion of a double pendulum interacting with a string. (English. Ukrainian original) Zbl 1272.70095 Int. Appl. Mech. 46, No. 12, 1428-1439 (2011); translation from Prikl. Mekh., Kiev 46, No. 12, 110-122 (2010). MSC: 70K20 74H45 74K05 PDF BibTeX XML Cite \textit{D. M. Lila}, Int. Appl. Mech. 46, No. 12, 1428--1439 (2011; Zbl 1272.70095); translation from Prikl. Mekh., Kiev 46, No. 12, 110--122 (2010) Full Text: DOI
Lila, D. M. Stability of the stationary motion of a spherical pendulum interacting with a string. (English. Ukrainian original) Zbl 1272.70094 Int. Appl. Mech. 46, No. 11, 1298-1310 (2011); translation from Prikl. Mekh., Kiev 46, No. 11, 101-114 (2010). MSC: 70K20 74H45 74K05 PDF BibTeX XML Cite \textit{D. M. Lila}, Int. Appl. Mech. 46, No. 11, 1298--1310 (2011; Zbl 1272.70094); translation from Prikl. Mekh., Kiev 46, No. 11, 101--114 (2010) Full Text: DOI
Lobas, L. G.; Ichans’kyj, V. Yu. Influence of the type of characteristics of elastic elements on a double pendulum limit cycles. (Ukrainian. English summary) Zbl 1224.70004 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2010, No. 3, 65-69 (2010). MSC: 70E55 PDF BibTeX XML Cite \textit{L. G. Lobas} and \textit{V. Yu. Ichans'kyj}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2010, No. 3, 65--69 (2010; Zbl 1224.70004)
Dubas, A. M. Bifurcations of equilibrium states of generalized Ziegler model of elastic bar. (Ukrainian. English summary) Zbl 1189.70009 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2009, No. 8, 54-57 (2009). MSC: 70E55 70K40 PDF BibTeX XML Cite \textit{A. M. Dubas}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2009, No. 8, 54--57 (2009; Zbl 1189.70009)
Pokorny, P. Stability condition for vertical oscillation of 3-dim heavy spring elastic pendulum. (English) Zbl 1229.70046 Regul. Chaotic Dyn. 13, No. 3, 155-165 (2008). MSC: 70G60 70K20 37J25 PDF BibTeX XML Cite \textit{P. Pokorny}, Regul. Chaotic Dyn. 13, No. 3, 155--165 (2008; Zbl 1229.70046) Full Text: DOI
Ichans’kyj, V. Yu. Limit cycles of a double pendulum with hard characteristics of elastic elements and a follower force. (Ukrainian. English summary) Zbl 1164.70308 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2008, No. 12, 71-73 (2008). MSC: 70E55 PDF BibTeX XML Cite \textit{V. Yu. Ichans'kyj}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2008, No. 12, 71--73 (2008; Zbl 1164.70308)
Holm, Darryl D. Geometric mechanics. Part I: Dynamics and symmetry. (English) Zbl 1160.70001 London: Imperial College Press (ISBN 978-1-84816-195-5/hbk; 978-1-84816-196-2/pbk). xx, 354 p. (2008). Reviewer: Ioan Bucataru (Iaşi) MSC: 70-01 70Hxx 70G45 PDF BibTeX XML Cite \textit{D. D. Holm}, Geometric mechanics. Part I: Dynamics and symmetry. London: Imperial College Press (2008; Zbl 1160.70001)
Lobas, L. G.; Kovalchuk, V. V.; Bambura, O. V. Effect of mixed characteristics of elastic elements on the equilibrium of an overturned pendulum. (Russian, English) Zbl 1164.70309 Prikl. Mekh., Kiev 43, No. 7, 107-113 (2007); translation in Int. Appl. Mech. 43, No. 7, 794-799 (2007). Reviewer: Julia A. Martynyuk (Kyïv) MSC: 70E55 70K50 PDF BibTeX XML Cite \textit{L. G. Lobas} et al., Prikl. Mekh., Kiev 43, No. 7, 107--113 (2007; Zbl 1164.70309); translation in Int. Appl. Mech. 43, No. 7, 794--799 (2007)
Linnér, Anders; Jerome, Joseph W. A unique graph of minimal elastic energy. (English) Zbl 1110.58009 Trans. Am. Math. Soc. 359, No. 5, 2021-2041 (2007). Reviewer: Themistocles M. Rassias (Athens) MSC: 58E25 49J30 58Z05 PDF BibTeX XML Cite \textit{A. Linnér} and \textit{J. W. Jerome}, Trans. Am. Math. Soc. 359, No. 5, 2021--2041 (2007; Zbl 1110.58009) Full Text: DOI
Chernov, A. M. Elastodynamics of the float navigational devices on the vibrating foundation with the absence end-wall stream of liquid. (Russian) Zbl 1134.70315 Prikladnaya matematika i mekhanika. Sbornik nauchnykh trudov. Ul’yanovsk: Ul’yanovskij Gosudarstvennyj Tekhnicheskij Universitet (ISBN 5-89146-526-4/pbk). 49-54 (2004). Reviewer: Yuri N. Sankin (Ul’yanovsk) MSC: 70J35 76D99 PDF BibTeX XML Cite \textit{A. M. Chernov}, in: Prikladnaya matematika i mekhanika. Sbornik nauchnykh trudov. Ul'yanovsk: Ul'yanovskij Gosudarstvennyj Tekhnicheskij Universitet. 49--54 (2004; Zbl 1134.70315)
Lynch, Peter; Houghton, Conor Pulsation and precession of the resonant swinging spring. (English) Zbl 1098.70540 Physica D 190, No. 1-2, 38-62 (2004). MSC: 70K99 74H45 PDF BibTeX XML Cite \textit{P. Lynch} and \textit{C. Houghton}, Physica D 190, No. 1--2, 38--62 (2004; Zbl 1098.70540) Full Text: DOI
Tuwankotta, J. M.; Quispel, G. R. W. Geometric numerical integration applied to the elastic pendulum at higher-order resonance. (English) Zbl 1107.37309 J. Comput. Appl. Math. 154, No. 1, 229-242 (2003). MSC: 37M15 65P10 70H08 70-08 PDF BibTeX XML Cite \textit{J. M. Tuwankotta} and \textit{G. R. W. Quispel}, J. Comput. Appl. Math. 154, No. 1, 229--242 (2003; Zbl 1107.37309) Full Text: DOI
Lynch, Peter Resonant motions of the three-dimensional elastic pendulum. (English) Zbl 1346.74085 Int. J. Non-Linear Mech. 37, No. 2, 345-367 (2002). MSC: 74H45 PDF BibTeX XML Cite \textit{P. Lynch}, Int. J. Non-Linear Mech. 37, No. 2, 345--367 (2002; Zbl 1346.74085) Full Text: DOI
Holm, Darryl D.; Lynch, Peter Stepwise precession of the resonant swinging spring. (English) Zbl 1140.37350 SIAM J. Appl. Dyn. Syst. 1, No. 1, 44-64 (2002). MSC: 37J15 37J35 70H06 37N05 37N15 PDF BibTeX XML Cite \textit{D. D. Holm} and \textit{P. Lynch}, SIAM J. Appl. Dyn. Syst. 1, No. 1, 44--64 (2002; Zbl 1140.37350) Full Text: DOI
Jamal, M.; Braikat, B.; Boutmir, S.; Damil, N.; Potier-Ferry, M. A high order implicit algorithm for solving instationary non-linear problems. (English) Zbl 1006.65089 Comput. Mech. 28, No. 5, 375-380 (2002). MSC: 65M06 65M12 74B20 74S20 35K55 35Q53 PDF BibTeX XML Cite \textit{M. Jamal} et al., Comput. Mech. 28, No. 5, 375--380 (2002; Zbl 1006.65089) Full Text: DOI
Schwab, A. L.; Meijaard, J. P. Small vibrations superimposed on a prescribed rigid body motion. (English) Zbl 1022.70003 Multibody Syst. Dyn. 8, No. 1, 29-50 (2002). Reviewer: Irina Alexandrovna Bolgrabskaya (Donetsk) MSC: 70E55 74H45 PDF BibTeX XML Cite \textit{A. L. Schwab} and \textit{J. P. Meijaard}, Multibody Syst. Dyn. 8, No. 1, 29--50 (2002; Zbl 1022.70003) Full Text: DOI
Schagerl, M.; Berger, A. On the appropriate treatment of singularly perturbed wave equations. (English) Zbl 1038.70017 ZAMM, Z. Angew. Math. Mech. 81, Suppl. 3, 623-624 (2001). Reviewer: Petre P. Teodorescu (Bucureşti) MSC: 70K70 70K60 PDF BibTeX XML Cite \textit{M. Schagerl} and \textit{A. Berger}, ZAMM, Z. Angew. Math. Mech. 81, 623--624 (2001; Zbl 1038.70017) Full Text: DOI
Bammer, Ferdinand; Troger, Hans On the stability of highly symmetric rotating systems. (English) Zbl 1002.74047 ZAMM, Z. Angew. Math. Mech. 81, Suppl. 2, 175-176 (2001). MSC: 74H55 74K10 74M20 PDF BibTeX XML Cite \textit{F. Bammer} and \textit{H. Troger}, ZAMM, Z. Angew. Math. Mech. 81, 175--176 (2001; Zbl 1002.74047) Full Text: DOI
Tuwankotta, J. M.; Verhulst, F. Symmetry and resonance in Hamiltonian systems. (English) Zbl 1004.70015 SIAM J. Appl. Math. 61, No. 4, 1369-1385 (2000). Reviewer: Messoud Efendiev (Berlin) MSC: 70H33 70K30 70H09 70K45 PDF BibTeX XML Cite \textit{J. M. Tuwankotta} and \textit{F. Verhulst}, SIAM J. Appl. Math. 61, No. 4, 1369--1385 (2000; Zbl 1004.70015) Full Text: DOI
Stronge, W. J. Impact mechanics. (English) Zbl 0961.74002 Cambridge: Cambridge University Press. 304 p. £42.50; $ 69.95 (2000). Reviewer: Piero Villaggio (Pisa) MSC: 74-02 74M20 70E18 74M15 70E55 70F35 PDF BibTeX XML Cite \textit{W. J. Stronge}, Impact mechanics. Cambridge: Cambridge University Press (2000; Zbl 0961.74002) Full Text: DOI
Pilipchuk, Valery N.; Ibrahim, Raouf A. Dynamics of a two-pendulum model with impact interaction and an elastic support. (English) Zbl 0977.70018 Nonlinear Dyn. 21, No. 3, 221-247 (2000). MSC: 70K99 70K28 PDF BibTeX XML Cite \textit{V. N. Pilipchuk} and \textit{R. A. Ibrahim}, Nonlinear Dyn. 21, No. 3, 221--247 (2000; Zbl 0977.70018) Full Text: DOI
Champneys, Alan R.; Fraser, W. Barrie The ‘Indian rope trick’ for a parametrically excited flexible rod: Linearized analysis. (English) Zbl 0974.74029 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 456, No. 1995, 553-570 (2000). Reviewer: Vyacheslav Pivovarchik (Odessa) MSC: 74H55 74K10 74H45 74H10 PDF BibTeX XML Cite \textit{A. R. Champneys} and \textit{W. B. Fraser}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 456, No. 1995, 553--570 (2000; Zbl 0974.74029) Full Text: DOI
Lobas, L. G.; Boruk, I. G. Stability domains of a two-link inverted mathematical pendulum in special force fields. (Ukrainian. English summary) Zbl 1054.70514 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 1999, No. 11, 74-78 (1999). Reviewer: O. Yu. Zharii (Kyïv) MSC: 70K20 PDF BibTeX XML Cite \textit{L. G. Lobas} and \textit{I. G. Boruk}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 1999, No. 11, 74--78 (1999; Zbl 1054.70514)
Georgiou, Ioannis T. On the global geometric structure of the dynamics of the elastic pendulum. (English) Zbl 0963.70013 Nonlinear Dyn. 18, No. 1, 51-68 (1999). Reviewer: S.Nocilla (Torino) MSC: 70K05 70K20 70K50 70K60 PDF BibTeX XML Cite \textit{I. T. Georgiou}, Nonlinear Dyn. 18, No. 1, 51--68 (1999; Zbl 0963.70013) Full Text: DOI
Beltzer, Abraham I. Variational and finite element methods. A symbolic computation approach. (English) Zbl 0703.73092 Berlin etc.: Springer-Verlag. xi, 254 p. DM 98.00 (1990). Reviewer: H.Bufler MSC: 74S30 74P10 74S05 74-01 49M15 74H45 PDF BibTeX XML Cite \textit{A. I. Beltzer}, Variational and finite element methods. A symbolic computation approach. Berlin etc.: Springer-Verlag (1990; Zbl 0703.73092)
Anderson, G. L.; Tadjbakhsh, I. G. Stabilization of Ziegler’s pendulum by means of the method of vibrational control. (English) Zbl 0681.70026 Applied mathematics and computing, Trans. 5th Army Conf., West Point, NY 1987, ARO Rep. 88-1, 787-843 (1988). MSC: 70J30 70Q05 PDF BibTeX XML
Cohen, H.; Sun, Q.-X. Plane motions of elastic pseudo-rigid pendulums. (English) Zbl 0669.73008 Solid Mech. Arch. 13, No. 3, 147-176 (1988). Reviewer: Y.Kivshar MSC: 74B20 70K30 74H45 PDF BibTeX XML Cite \textit{H. Cohen} and \textit{Q. X. Sun}, Solid Mech. Arch. 13, No. 3, 147--176 (1988; Zbl 0669.73008)
Lukovskij, I. A. (ed.) Applied problems of dynamics and of the stability of mechanical systems. Collection of scientific works. (Prikladnye zadachi dinamiki i ustojchivosti mnogomernykh sistem. Sbornik nauchnykh trudov). (Russian) Zbl 0651.76004 Kiev: Institut Matematiki AN USSR. 143 p. R. 1.05 (1987). MSC: 76-06 74-06 93-06 PDF BibTeX XML
Kummer, Martin On resonant Hamiltonian systems with finitely many degrees of freedom. (English) Zbl 0619.70021 Local and global methods of nonlinear dynamics, Proc. Workshop, Silver Spring/Md. 1984, Lect. Notes Phys. 252, 19-31 (1986). Reviewer: C.Chernyatin MSC: 70K30 70H05 70G10 70F05 37J40 37C75 PDF BibTeX XML
Katz, A.; Schuss, Z. Reliability of elastic structures driven by random loads. (English) Zbl 0577.73089 SIAM J. Appl. Math. 45, 383-402 (1985). MSC: 74H50 62N05 70L05 74K10 PDF BibTeX XML Cite \textit{A. Katz} and \textit{Z. Schuss}, SIAM J. Appl. Math. 45, 383--402 (1985; Zbl 0577.73089) Full Text: DOI
Scheidl, R.; Troger, H.; Zeman, K. Coupled flutter and divergence bifurcation of a double pendulum. (English) Zbl 0563.70024 Int. J. Non-Linear Mech. 19, 163-176 (1984). MSC: 70K20 PDF BibTeX XML Cite \textit{R. Scheidl} et al., Int. J. Non-Linear Mech. 19, 163--176 (1984; Zbl 0563.70024) Full Text: DOI
Scheidl, R. Über die Divergenzverzweigung beim Doppelpendel mit tangentialer Folgelast und elastischer Endlagerung. (German) Zbl 0537.70023 Z. Angew. Math. Mech. 63, No. 4, T90-T93 (1983). MSC: 70K20 PDF BibTeX XML Cite \textit{R. Scheidl}, Z. Angew. Math. Mech. 63, T90--T93 (1983; Zbl 0537.70023)
Hsu, L. Analysis of critical and post-critical behaviour of nonlinear dynamical systems II: Divergence and flutter. (English) Zbl 0522.73039 J. Sound Vib. 89, 183-194 (1983). MSC: 74H55 37G99 74F10 PDF BibTeX XML Cite \textit{L. Hsu}, J. Sound Vib. 89, 183--194 (1983; Zbl 0522.73039) Full Text: DOI
Koshlyakov, V. N. On the theory of gyroscopic compasses in the light of analogies with elastic systems. (Russian) Zbl 0522.70008 Mekh. Giroskopicheskikh Sist. 1, 3-11 (1982). MSC: 70E05 70K20 PDF BibTeX XML Cite \textit{V. N. Koshlyakov}, Mekh. Giroskopicheskikh Sist. 1, 3--11 (1982; Zbl 0522.70008)
Marsden, Jerrold E. Lectures on geometric methods in mathematical physics. (English) Zbl 0485.70001 CBMS-NSF Regional Conference Series in Applied Mathematics 37. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 0-89871-170-3). v, 97 p. (1981). MSC: 70-02 70A05 58D30 37J35 37K10 35Q05 74Bxx 70E15 70H05 83C05 PDF BibTeX XML Cite \textit{J. E. Marsden}, Lectures on geometric methods in mathematical physics. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (1981; Zbl 0485.70001)
Breitenberger, Ernst; Mueller, Robert D. The elastic pendulum: A nonlinear paradigm. (English) Zbl 0464.70025 J. Math. Phys. 22, 1196-1210 (1981). MSC: 70K30 70K20 PDF BibTeX XML Cite \textit{E. Breitenberger} and \textit{R. D. Mueller}, J. Math. Phys. 22, 1196--1210 (1981; Zbl 0464.70025) Full Text: DOI
Kiusalaas, J.; Davis, H. E. On the stability of elastic systems under retarded follower forces. (English) Zbl 0187.23404 Int. J. Solids Struct. 6, 399-409 (1970). MSC: 74H55 PDF BibTeX XML Cite \textit{J. Kiusalaas} and \textit{H. E. Davis}, Int. J. Solids Struct. 6, 399--409 (1970; Zbl 0187.23404) Full Text: DOI
Cheshankov, Bozhidar Periodische Bewegungen eines elastischen Pendels mit aufgewickeltem Faden. (Bulgarian. Russian summary) Zbl 0309.70006 God. Vissh. Tekh. Uchebn. Zaved., Mat. 1(1964), No. 1, 73-82 (1965). MSC: 70F99 70K99 PDF BibTeX XML Cite \textit{B. Cheshankov}, God. Vissh. Tekh. Uchebn. Zaved., Mat. 1, No. 1, 73--82 (1965; Zbl 0309.70006)