Multiplicity of forced oscillations for the spherical pendulum acted on by a retarded periodic force
We prove a multiplicity result for forced oscillations of a spherical pendulum (that is, a massive point moving on a sphere) subject to a periodic action, with or without friction, allowed to depend on the whole past of the motion. The approach is based on topological methods. In particular, when th...
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| Published in | Nonlinear analysis Vol. 151; pp. 252 - 264 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
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01.03.2017
Elsevier BV |
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| ISSN | 0362-546X 1873-5215 |
| DOI | 10.1016/j.na.2016.12.006 |
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| Abstract | We prove a multiplicity result for forced oscillations of a spherical pendulum (that is, a massive point moving on a sphere) subject to a periodic action, with or without friction, allowed to depend on the whole past of the motion. The approach is based on topological methods.
In particular, when the unperturbed forcing term is the gravity, we obtain two harmonic forced oscillations regardless of the presence of friction and of the form of the perturbing force field. |
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| AbstractList | We prove a multiplicity result for forced oscillations of a spherical pendulum (that is, a massive point moving on a sphere) subject to a periodic action, with or without friction, allowed to depend on the whole past of the motion. The approach is based on topological methods. In particular, when the unperturbed forcing term is the gravity, we obtain two harmonic forced oscillations regardless of the presence of friction and of the form of the perturbing force field. We prove a multiplicity result for forced oscillations of a spherical pendulum (that is, a massive point moving on a sphere) subject to a periodic action, with or without friction, allowed to depend on the whole past of the motion. The approach is based on topological methods. In particular, when the unperturbed forcing term is the gravity, we obtain two harmonic forced oscillations regardless of the presence of friction and of the form of the perturbing force field. |
| Author | Spadini, Marco Calamai, Alessandro Pera, Maria Patrizia |
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| References | Furi (br000055) 1995; vol. 472 Polekhin (br000140) 2015; 128 Furi, Pera, Spadini (br000075) 2005 Benevieri, Calamai, Furi, Pera (br000015) 2011; 23 Furi, Spadini (br000095) 1999; 154 Furi, Spadini (br000085) 1997; 29 Boscaggin, Ortega, Zanolin (br000040) 2014; 102 Mawhin, Willem (br000130) 1984; 52 Benevieri, Calamai, Furi, Pera (br000025) 2013; 33 Furi, Pera, Spadini (br000080) 2011; 15 Furi, Spadini (br000090) 1998; 11 Mawhin (br000115) 1998 Furi, Pera (br000060) 1990; 4 Hale, Verduyn Lunel (br000100) 1993; vol. 99 Furi, Pera (br000065) 1991; vol. 1475 Mawhin (br000120) 2004 Katriel (br000105) 1998; 34 Benci (br000005) 1986; 63 Furi, Pera, Spadini (br000070) 2000; 113 Lewicka, Spadini (br000110) 1999; 6 Bisconti, Spadini (br000035) 2015; 38 Benevieri, Calamai, Furi, Pera (br000030) 2014; 16 Mawhin (br000125) 2014; 47 Fonda, Toader (br000050) 2012; 12 Ureña (br000145) 2005; 302 Milnor (br000135) 1997 Cronin (br000045) 1994; vol. 180 Benevieri, Calamai, Furi, Pera (br000020) 2013; 2013 Benci, Degiovanni (br000010) 1990; vol. 4 Bisconti (10.1016/j.na.2016.12.006_br000035) 2015; 38 Katriel (10.1016/j.na.2016.12.006_br000105) 1998; 34 Furi (10.1016/j.na.2016.12.006_br000065) 1991; vol. 1475 Benevieri (10.1016/j.na.2016.12.006_br000015) 2011; 23 Ureña (10.1016/j.na.2016.12.006_br000145) 2005; 302 Furi (10.1016/j.na.2016.12.006_br000080) 2011; 15 Benevieri (10.1016/j.na.2016.12.006_br000030) 2014; 16 Mawhin (10.1016/j.na.2016.12.006_br000115) 1998 Furi (10.1016/j.na.2016.12.006_br000075) 2005 Furi (10.1016/j.na.2016.12.006_br000085) 1997; 29 Benci (10.1016/j.na.2016.12.006_br000005) 1986; 63 Hale (10.1016/j.na.2016.12.006_br000100) 1993; vol. 99 Furi (10.1016/j.na.2016.12.006_br000090) 1998; 11 Mawhin (10.1016/j.na.2016.12.006_br000130) 1984; 52 Boscaggin (10.1016/j.na.2016.12.006_br000040) 2014; 102 Furi (10.1016/j.na.2016.12.006_br000055) 1995; vol. 472 Milnor (10.1016/j.na.2016.12.006_br000135) 1997 Cronin (10.1016/j.na.2016.12.006_br000045) 1994; vol. 180 Furi (10.1016/j.na.2016.12.006_br000095) 1999; 154 Furi (10.1016/j.na.2016.12.006_br000060) 1990; 4 Lewicka (10.1016/j.na.2016.12.006_br000110) 1999; 6 Polekhin (10.1016/j.na.2016.12.006_br000140) 2015; 128 Mawhin (10.1016/j.na.2016.12.006_br000120) 2004 Furi (10.1016/j.na.2016.12.006_br000070) 2000; 113 Benevieri (10.1016/j.na.2016.12.006_br000020) 2013; 2013 Mawhin (10.1016/j.na.2016.12.006_br000125) 2014; 47 Benci (10.1016/j.na.2016.12.006_br000010) 1990; vol. 4 Benevieri (10.1016/j.na.2016.12.006_br000025) 2013; 33 Fonda (10.1016/j.na.2016.12.006_br000050) 2012; 12 |
| References_xml | – volume: 47 start-page: 124 year: 2014 end-page: 130 ident: br000125 article-title: The implicit function theorem and its substitutes in Poincaré’s qualitative theory of differential equations publication-title: Stud. Hist. Philos. Sci. B Stud. Hist. Philos. Modern Phys. – volume: 128 start-page: 100 year: 2015 end-page: 105 ident: br000140 article-title: Forced oscillations of a massive point on a compact surface with a boundary publication-title: Nonlinear Anal. – volume: vol. 1475 start-page: 176 year: 1991 end-page: 182 ident: br000065 article-title: The forced spherical pendulum does have forced oscillations publication-title: Delay Differential Equations and Dynamical Systems (Claremont, CA, 1990) – volume: 11 start-page: 147 year: 1998 end-page: 157 ident: br000090 article-title: Multiplicity of forced oscillations for the spherical pendulum publication-title: Topol. Methods Nonlinear Anal. – volume: 12 start-page: 395 year: 2012 end-page: 408 ident: br000050 article-title: Periodic solutions of pendulum-like Hamiltonian systems in the plane publication-title: Adv. Nonlinear Stud. – volume: 4 start-page: 381 year: 1990 end-page: 390 ident: br000060 article-title: On the existence of forced oscillations for the spherical pendulum publication-title: Boll. Un. Mat. Ital. B (7) – start-page: 741 year: 2005 end-page: 782 ident: br000075 article-title: The fixed point index of the Poincaré translation operator on differentiable manifolds publication-title: Handbook of Topological Fixed Point Theory – volume: vol. 99 year: 1993 ident: br000100 publication-title: Introduction to Functional-Differential Equations – volume: 34 start-page: 687 year: 1998 end-page: 699 ident: br000105 article-title: Many periodic solutions for pendulum-type equations publication-title: Nonlinear Anal. – volume: 302 start-page: 318 year: 2005 end-page: 341 ident: br000145 article-title: Using closed orbits to bifurcate many periodic solutions for pendulum-type equations publication-title: J. Math. Anal. Appl. – volume: 16 start-page: 273 year: 2014 end-page: 300 ident: br000030 article-title: Global continuation of forced oscillations of retarded motion equations on manifolds publication-title: J. Fixed Point Theory Appl. – volume: vol. 4 start-page: 395 year: 1990 end-page: 411 ident: br000010 article-title: Periodic solutions of dissipative dynamical systems publication-title: Variational Methods (Paris, 1988) – volume: 154 start-page: 96 year: 1999 end-page: 106 ident: br000095 article-title: Branches of forced oscillations for periodically perturbed second order autonomous ODEs on manifolds publication-title: J. Differential Equations – volume: 113 start-page: 241 year: 2000 end-page: 254 ident: br000070 article-title: Forced oscillations on manifolds and multiplicity results for periodically perturbed autonomous systems publication-title: J. Comput. Appl. Math. – year: 1997 ident: br000135 publication-title: Topology from the Differentiable Viewpoint – volume: vol. 472 start-page: 89 year: 1995 end-page: 127 ident: br000055 article-title: Second order differential equations on manifolds and forced oscillations publication-title: Topological Methods in Differential Equations and Inclusions (Montreal, PQ, 1994) – volume: 38 start-page: 4760 year: 2015 end-page: 4773 ident: br000035 article-title: About the notion of non- publication-title: Math. Methods Appl. Sci. – volume: vol. 180 year: 1994 ident: br000045 publication-title: Differential Equations: Introduction and Qualitative Theory – volume: 29 start-page: 963 year: 1997 end-page: 970 ident: br000085 article-title: On the set of harmonic solutions of periodically perturbed autonomous differential equations on manifolds publication-title: Nonlinear Anal. – start-page: 115 year: 1998 end-page: 145 ident: br000115 article-title: Seventy-five years of global analysis around the forced pendulum equation publication-title: Proceedings of Equadiff 9 – start-page: 533 year: 2004 end-page: 589 ident: br000120 article-title: Global results for the forced pendulum equation publication-title: Handbook of Differential Equations, Vol. 1 – volume: 52 start-page: 264 year: 1984 end-page: 287 ident: br000130 article-title: Multiple solutions of the periodic boundary value problem for some forced pendulum-type equations publication-title: J. Differential Equations – volume: 2013 start-page: 19 year: 2013 ident: br000020 article-title: Global continuation of periodic solutions for retarded functional differential equations on manifolds publication-title: Bound. Value Probl. – volume: 15 start-page: 381 year: 2011 end-page: 394 ident: br000080 article-title: Periodic solutions of retarded functional perturbations of autonomous differential equations on manifolds publication-title: Commun. Appl. Anal. – volume: 23 start-page: 541 year: 2011 end-page: 549 ident: br000015 article-title: On the existence of forced oscillations for the spherical pendulum acted on by a retarded periodic force publication-title: J. Dynam. Differential Equations – volume: 33 start-page: 27 year: 2013 end-page: 46 ident: br000025 article-title: On general properties of retarded functional differential equations on manifolds publication-title: Discrete Contin. Dyn. Syst. – volume: 63 start-page: 135 year: 1986 end-page: 161 ident: br000005 article-title: Periodic solutions of Lagrangian systems on a compact manifold publication-title: J. Differential Equations – volume: 6 start-page: 357 year: 1999 end-page: 369 ident: br000110 article-title: On the genericity of the multiplicity results for forced oscillations on compact manifolds publication-title: NoDEA Nonlinear Differential Equations Appl. – volume: 102 start-page: 459 year: 2014 end-page: 468 ident: br000040 article-title: Subharmonic solutions of the forced pendulum equation: a symplectic approach publication-title: Arch. Math. (Basel) – volume: vol. 4 start-page: 395 year: 1990 ident: 10.1016/j.na.2016.12.006_br000010 article-title: Periodic solutions of dissipative dynamical systems – volume: 2013 start-page: 19 issue: 21 year: 2013 ident: 10.1016/j.na.2016.12.006_br000020 article-title: Global continuation of periodic solutions for retarded functional differential equations on manifolds publication-title: Bound. Value Probl. – volume: vol. 99 year: 1993 ident: 10.1016/j.na.2016.12.006_br000100 – start-page: 741 year: 2005 ident: 10.1016/j.na.2016.12.006_br000075 article-title: The fixed point index of the Poincaré translation operator on differentiable manifolds – volume: 4 start-page: 381 issue: 2 year: 1990 ident: 10.1016/j.na.2016.12.006_br000060 article-title: On the existence of forced oscillations for the spherical pendulum publication-title: Boll. Un. Mat. Ital. B (7) – volume: 38 start-page: 4760 issue: 18 year: 2015 ident: 10.1016/j.na.2016.12.006_br000035 article-title: About the notion of non-T-resonance and applications to topological multiplicity results for ODEs on differentiable manifolds publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.3390 – volume: vol. 180 year: 1994 ident: 10.1016/j.na.2016.12.006_br000045 – volume: 12 start-page: 395 issue: 2 year: 2012 ident: 10.1016/j.na.2016.12.006_br000050 article-title: Periodic solutions of pendulum-like Hamiltonian systems in the plane publication-title: Adv. Nonlinear Stud. doi: 10.1515/ans-2012-0210 – volume: 11 start-page: 147 issue: 1 year: 1998 ident: 10.1016/j.na.2016.12.006_br000090 article-title: Multiplicity of forced oscillations for the spherical pendulum publication-title: Topol. Methods Nonlinear Anal. doi: 10.12775/TMNA.1998.009 – volume: 16 start-page: 273 issue: 1–2 year: 2014 ident: 10.1016/j.na.2016.12.006_br000030 article-title: Global continuation of forced oscillations of retarded motion equations on manifolds publication-title: J. Fixed Point Theory Appl. doi: 10.1007/s11784-015-0215-6 – volume: 128 start-page: 100 year: 2015 ident: 10.1016/j.na.2016.12.006_br000140 article-title: Forced oscillations of a massive point on a compact surface with a boundary publication-title: Nonlinear Anal. doi: 10.1016/j.na.2015.07.022 – volume: 302 start-page: 318 issue: 2 year: 2005 ident: 10.1016/j.na.2016.12.006_br000145 article-title: Using closed orbits to bifurcate many periodic solutions for pendulum-type equations publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2003.11.057 – volume: 154 start-page: 96 issue: 1 year: 1999 ident: 10.1016/j.na.2016.12.006_br000095 article-title: Branches of forced oscillations for periodically perturbed second order autonomous ODEs on manifolds publication-title: J. Differential Equations doi: 10.1006/jdeq.1998.3557 – volume: 34 start-page: 687 issue: 5 year: 1998 ident: 10.1016/j.na.2016.12.006_br000105 article-title: Many periodic solutions for pendulum-type equations publication-title: Nonlinear Anal. doi: 10.1016/S0362-546X(97)00609-3 – volume: 113 start-page: 241 issue: 1–2 year: 2000 ident: 10.1016/j.na.2016.12.006_br000070 article-title: Forced oscillations on manifolds and multiplicity results for periodically perturbed autonomous systems publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(99)00259-9 – volume: 23 start-page: 541 year: 2011 ident: 10.1016/j.na.2016.12.006_br000015 article-title: On the existence of forced oscillations for the spherical pendulum acted on by a retarded periodic force publication-title: J. Dynam. Differential Equations doi: 10.1007/s10884-010-9201-2 – volume: 63 start-page: 135 year: 1986 ident: 10.1016/j.na.2016.12.006_br000005 article-title: Periodic solutions of Lagrangian systems on a compact manifold publication-title: J. Differential Equations doi: 10.1016/0022-0396(86)90045-8 – volume: 6 start-page: 357 issue: 4 year: 1999 ident: 10.1016/j.na.2016.12.006_br000110 article-title: On the genericity of the multiplicity results for forced oscillations on compact manifolds publication-title: NoDEA Nonlinear Differential Equations Appl. doi: 10.1007/s000300050008 – volume: vol. 1475 start-page: 176 year: 1991 ident: 10.1016/j.na.2016.12.006_br000065 article-title: The forced spherical pendulum does have forced oscillations – volume: 47 start-page: 124 year: 2014 ident: 10.1016/j.na.2016.12.006_br000125 article-title: The implicit function theorem and its substitutes in Poincaré’s qualitative theory of differential equations publication-title: Stud. Hist. Philos. Sci. B Stud. Hist. Philos. Modern Phys. doi: 10.1016/j.shpsb.2014.01.006 – year: 1997 ident: 10.1016/j.na.2016.12.006_br000135 – volume: 52 start-page: 264 issue: 2 year: 1984 ident: 10.1016/j.na.2016.12.006_br000130 article-title: Multiple solutions of the periodic boundary value problem for some forced pendulum-type equations publication-title: J. Differential Equations doi: 10.1016/0022-0396(84)90180-3 – volume: 33 start-page: 27 issue: 1 year: 2013 ident: 10.1016/j.na.2016.12.006_br000025 article-title: On general properties of retarded functional differential equations on manifolds publication-title: Discrete Contin. Dyn. Syst. doi: 10.3934/dcds.2013.33.27 – start-page: 533 year: 2004 ident: 10.1016/j.na.2016.12.006_br000120 article-title: Global results for the forced pendulum equation – volume: 102 start-page: 459 issue: 5 year: 2014 ident: 10.1016/j.na.2016.12.006_br000040 article-title: Subharmonic solutions of the forced pendulum equation: a symplectic approach publication-title: Arch. Math. (Basel) doi: 10.1007/s00013-014-0644-2 – volume: 15 start-page: 381 issue: 2–4 year: 2011 ident: 10.1016/j.na.2016.12.006_br000080 article-title: Periodic solutions of retarded functional perturbations of autonomous differential equations on manifolds publication-title: Commun. Appl. Anal. – volume: vol. 472 start-page: 89 year: 1995 ident: 10.1016/j.na.2016.12.006_br000055 article-title: Second order differential equations on manifolds and forced oscillations – volume: 29 start-page: 963 issue: 8 year: 1997 ident: 10.1016/j.na.2016.12.006_br000085 article-title: On the set of harmonic solutions of periodically perturbed autonomous differential equations on manifolds publication-title: Nonlinear Anal. doi: 10.1016/S0362-546X(96)00296-9 – start-page: 115 year: 1998 ident: 10.1016/j.na.2016.12.006_br000115 article-title: Seventy-five years of global analysis around the forced pendulum equation |
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| SubjectTerms | Degree of a tangent vector field Differential equations Forced motion on manifolds Friction Gravitation Mathematical analysis Multiplicity of periodic solutions Oscillations Oscillators Retarded functional differential equations |
| Title | Multiplicity of forced oscillations for the spherical pendulum acted on by a retarded periodic force |
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