The stability of the rotation of a heavy body with a viscous filling

Dosayev, M.Z.; Самсонов, В. А.

doi:10.1016/s0021-8928(02)00051-5

Cited by 11 publications

(8 citation statements)

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“…7 to describe the motion of the system. The angular momentum vector G s of the shell about to the centre of mass C is related to the angular velocity of the body by the expression where J s is the inertia tensor of the shell relative to the Cx 1 x 2 x 3 axis system, and A s and C s are the equatorial and axial moments of inertia of the shell about to the centre of mass of the system.…”

Section: Statement Of the Problemmentioning

confidence: 99%

Permanent rotations of a body with a viscous filler suspended on a rod

Karapetyan¹,

Sumin²

2008

Journal of Applied Mathematics and Mechanics

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Section: Statement Of the Problemmentioning

confidence: 99%

Permanent rotations of a body with a viscous filler suspended on a rod

Karapetyan¹,

Sumin²

2008

Journal of Applied Mathematics and Mechanics

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“…Investigations of the liquid-filled gyrostat are reviewed in Gray [2], Rumyantsev [12], Moiseev and Rumyantsev [13], Wang and Liu [14] amongst others. The investigations on applications of dynamics of the liquid-filled solid body in the spinning vehicles may be found in Stewartson [15], Wedemeyer [16], Pfeiffer [17], Dosaev and Samsonov [18] amongst others.…”

Section: Introductionmentioning

confidence: 99%

On the Chaotic Instability of a Nonsliding Liquid-Filled Top with a Small Spheroidal Base via Melnikov-Holmes-Marsden Integrals

2006

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Chaotic orientations of a top containing a fluid filled cavity are investigated analytically and numerically under small perturbations. The top spins and rolls in nonsliding contact with a rough horizontal plane and the fluid in the ellipsoidal shaped cavity is considered to be ideal and describable by finite degrees of freedom. A Hamiltonian structure is established to facilitate the application of Melnikov-Holmes-Marsden (MHM) integrals. In particular, chaotic motion of the liquid-filled top is identified to be arisen from the transversal intersections between the stable and unstable manifolds of an approximated, disturbed flow of the liquid-filled top via the MHM integrals. The developed analytical criteria are crosschecked with numerical simulations via the 4th Runge-Kutta algorithms with adaptive time steps.

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“…A phenomenological model of internal viscous friction was proposed in [2] and this model was tested in linear problems of the description of small oscillations in the neighbourhood of uniform rotations of a system around a vertically situated axis of symmetry. This model is used below to construct bifurcation diagrams of the steady motions of a symmetrical heavy body with a viscous filler (a nonlinear problem) which, together with the above-mentioned motions, includes uniform rotations around the vertical when the axis of symmetry of the body is in an inclined position.…”

mentioning

confidence: 99%