Motions of a Powered Top with a Spherical Tip on a Curved Surface
The purpose of this article is to model the dynamics of a top with a finite radius tip on a curved basin in a gravitational field without (and with) energy addition and dissipation. This is an extension of a very general and classical problem and requires development of a method for treating the dyn...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1995-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.3233/SAV-1995-2103 |
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| _version_ | 1832550019439263744 |
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| author | David C. Meeker Miles A. Townsend |
| author_facet | David C. Meeker Miles A. Townsend |
| author_sort | David C. Meeker |
| collection | DOAJ |
| description | The purpose of this article is to model the dynamics of a top with a finite radius tip on a curved basin in a gravitational field without (and with) energy addition and dissipation. This is an extension of a very general and classical problem and requires development of a method for treating the dynamical interactions between the two curved surfaces. The full nonlinear equations of motion are indicated; however, these equations are complex and do not show the dominant mechanisms that define the system motions. A novel method of “partial linearization” is employed that reduces the equations of motion to a relevant and tractable form in which these mechanisms are clearly exposed. The model and related results are compared with relevant examples from the literature. The movement of the top is simulated by an integration of the fully nonlinear equations of motion and compared with the partially linearized results. |
| format | Article |
| id | doaj-art-989169cef84a401b9fdbf07253443532 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 1995-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-989169cef84a401b9fdbf072534435322025-02-03T06:07:58ZengWileyShock and Vibration1070-96221875-92031995-01-0121233210.3233/SAV-1995-2103Motions of a Powered Top with a Spherical Tip on a Curved SurfaceDavid C. Meeker0Miles A. Townsend1Department of Mechanical, Aerospace, and Nuclear Engineering University of Virginia, Charlottesville, VA 22903, USADepartment of Mechanical, Aerospace, and Nuclear Engineering University of Virginia, Charlottesville, VA 22903, USAThe purpose of this article is to model the dynamics of a top with a finite radius tip on a curved basin in a gravitational field without (and with) energy addition and dissipation. This is an extension of a very general and classical problem and requires development of a method for treating the dynamical interactions between the two curved surfaces. The full nonlinear equations of motion are indicated; however, these equations are complex and do not show the dominant mechanisms that define the system motions. A novel method of “partial linearization” is employed that reduces the equations of motion to a relevant and tractable form in which these mechanisms are clearly exposed. The model and related results are compared with relevant examples from the literature. The movement of the top is simulated by an integration of the fully nonlinear equations of motion and compared with the partially linearized results.http://dx.doi.org/10.3233/SAV-1995-2103 |
| spellingShingle | David C. Meeker Miles A. Townsend Motions of a Powered Top with a Spherical Tip on a Curved Surface Shock and Vibration |
| title | Motions of a Powered Top with a Spherical Tip on a Curved Surface |
| title_full | Motions of a Powered Top with a Spherical Tip on a Curved Surface |
| title_fullStr | Motions of a Powered Top with a Spherical Tip on a Curved Surface |
| title_full_unstemmed | Motions of a Powered Top with a Spherical Tip on a Curved Surface |
| title_short | Motions of a Powered Top with a Spherical Tip on a Curved Surface |
| title_sort | motions of a powered top with a spherical tip on a curved surface |
| url | http://dx.doi.org/10.3233/SAV-1995-2103 |
| work_keys_str_mv | AT davidcmeeker motionsofapoweredtopwithasphericaltiponacurvedsurface AT milesatownsend motionsofapoweredtopwithasphericaltiponacurvedsurface |