The stability and branching of the permanent rotations of a rigid body with a fluid filling

Karapetyan, A.V.; Самсонов, В. А.; Sumin, T.S.

doi:10.1016/j.jappmathmech.2004.11.011

Cited by 6 publications

(3 citation statements)

References 1 publication

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“…, (4) in which characterizing the uniform rotation of the considered body about x -axis that coincides with the vertical.…”

Section: S S Nmentioning

confidence: 99%

“…The stability of a rigid body has shed the attention of outstanding researchers during the last seven decades whether if the body contains fluid [1][2][3][4] or under the action of attracting center [5][6][7][8][9][10][11][12][13]. The stability of the rotational motion of a solid containing an ideal incompressible homogenous fluid filled entirely or partially was studied in [1] and [2].…”

Section: Introductionmentioning

confidence: 99%

“…The sufficient conditions for the stability of the studied motions are achieved. The permanent rotations and their stability for same problem were discussed in [4].…”

Section: Introductionmentioning

confidence: 99%

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The necessary and sufficient condition for the stability of a rigid body

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“…, (4) in which characterizing the uniform rotation of the considered body about x -axis that coincides with the vertical.…”

Section: S S Nmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The necessary and sufficient condition for the stability of a rigid body

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Asymptotic properties of the motions of a heavy gyroscope with internal dissipation

Aduyenko¹,

Amel’kin²

2014

Journal of Applied Mathematics and Mechanics

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Lord Kelvin’s gyrostat and its analogs in physics, including the Lorenz model

Tong¹

2009

American Journal of Physics

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A gyrostat is a system of bodies whose relative motion does not alter the intrinsic mass distribution of the system. A solid gyrostat is an arbitrary rigid body attached to one or more axisymmetric rotors with their axes fixed in the carrier. A liquid gyrostat is a cavity in a rotating rigid body filled with an inviscid, homogeneous fluid. For certain conditions, gyrostats obey the Volterra equations of motion, a generalization of the Euler equations for a rigid body rotating about a fixed point. The Lorenz model is equivalent to a special case of a gyrostat in a forced, dissipative regime, as is its laboratory analog, the Malkus water wheel. Over a century ago, Lord Kelvin, the gyrostat’s inventor, attempted to formulate mechanical models of the elasticity of matter and the ether, using lattices of linked gyrostats. Opportunities for using gyrostats in the teaching of undergraduate mechanics, nonlinear dynamics, and fluid dynamics are discussed.

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The stability and branching of the permanent rotations of a rigid body with a fluid filling

Cited by 6 publications

References 1 publication

The necessary and sufficient condition for the stability of a rigid body

The necessary and sufficient condition for the stability of a rigid body

Asymptotic properties of the motions of a heavy gyroscope with internal dissipation

Lord Kelvin’s gyrostat and its analogs in physics, including the Lorenz model

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