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Phase Space of Rolling Solutions of the Tippe Top
Репозиторій DSpace/Manakin
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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Phase Space of Rolling Solutions of the Tippe Top
Інший ID:
2000 Mathematics Subject Classification: 70E18; 70E40; 70F25; 70K05
Посилання:
Phase Space of Rolling Solutions of the Tippe Top / S.T. Glad, D. Petersson, S. Rauch-Wojciechowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 14 назв. — англ.
Підтримка:
This paper is a contribution to the Vadim Kuznetsov Memorial Issue ‘Integrable Systems and Related Topics’. The authors would like to thank referees for useful suggestions and pointing some references.
Дата:
2007
Переглядів:
474
Завантажень:
228
Анотація:
Equations of motion of an axially symmetric sphere rolling and sliding on a plane are usually taken as model of the tippe top. We study these equations in the nonsliding regime both in the vector notation and in the Euler angle variables when they admit three integrals of motion that are linear and quadratic in momenta. In the Euler angle variables (θ,φ,ψ) these integrals give separation equations that have the same structure as the equations of the Lagrange top. It makes it possible to describe the whole space of solutions by representing them in the space of parameters (D,λ,E) being constant values of the integrals of motion.
