Representation of solutions to the problem of the motion of a heavy rigid body in the Kovalevskaya case in terms of Weierstrass $ \zeta$- and $ \wp$-functions and nonintegrability of the Hess case by quadratures

2016 ◽  
Vol 207 (7) ◽  
pp. 889-914 ◽  
Author(s):  
A V Belyaev
Keyword(s):  
Rigid Body ◽  
Heavy Rigid Body ◽  
Representation Of Solutions ◽  
Kovalevskaya Case

scholarly journals On the motion of a heavy rigid body in two special cases of S.V.Kovalevskaya’s solution

2018 ◽  
Vol 14 (1) ◽  
pp. 123-138
Author(s):  
Г.В. Горр ◽  
◽  
Е.К. Щетинина ◽  
Keyword(s):  
Rigid Body ◽  
Heavy Rigid Body ◽  
Special Cases

Remarks on the Covering of the Possible Motion Area by Solutions in Rigid Body Systems

2019 ◽  
Vol 20 (3-4) ◽  
pp. 293-302
Author(s):  
Ivan Polekhin
Keyword(s):  
Fixed Point ◽  
Rigid Body ◽  
Integrable Case ◽  
Analytical Results ◽  
Routh Reduction ◽  
Gyroscopic Forces ◽  
Kovalevskaya Case

AbstractThe problem of motion of a rigid body with a fixed point is considered. We study qualitatively the solutions of the system after Routh reduction. For the Lagrange integrable case, we show that the trajectories of solutions starting at the boundary of a possible motion area can both cover and not cover the entire possible motion area. It distinguishes these systems from the systems without gyroscopic forces, where the trajectories always cover the possible motion area. We also present some numerical and analytical results on the same matter for the Kovalevskaya case.

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