Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012, Number 4, Pages 44–47
This article is cited in 4 scientific papers (total in 4 papers)
Complete list of first integrals for dynamic equations of motion of a solid body in a resisting medium with consideration of linear damping
M. V. Shamolin
Lomonosov Moscow State University, Institute of Mechanics
A new case of integrability in the spatial problem of rigid body motion with consideration of the nonconservative moment of forces is discussed. A nonconservative force field of action of the medium on the body is constructed. Contrary to some previous author's works, a linear dependence of this field on the angular velocity is taken into account, although the introducing of this dependence into the components of such a field is not obvious.
rigid body, resisting medium, dynamic equations, phase space, transcendental first integral.
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Moscow University Mechanics Bulletin, 2012, 67:4, 92–95
M. V. Shamolin, “Complete list of first integrals for dynamic equations of motion of a solid body in a resisting medium with consideration of linear damping”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012, no. 4, 44–47; Moscow University Mechanics Bulletin, 67:4 (2012), 92–95
Citation in format AMSBIB
\paper Complete list of first integrals for dynamic equations of motion of a solid body in a resisting medium with consideration of linear damping
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\jour Moscow University Mechanics Bulletin
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M. V. Shamolin, “Integrable cases in the dynamics of a multi-dimensional rigid body in a nonconservative field in the presence of a tracking force”, J. Math. Sci., 214:6 (2016), 865–891
M. V. Shamolin, “Integrable variable dissipation systems on the tangent bundle of a multi-dimensional sphere and some applications”, J. Math. Sci., 230:2 (2018), 185–353
M. V. Shamolin, “Integrable systems on the tangent bundle of a multi-dimensional sphere”, J. Math. Sci. (N. Y.), 234:4 (2018), 548–590
M. V. Shamolin, “Integrable nonconservative dynamical systems on the tangent bundle of the multidimensional sphere”, Differ. Equ., 52:6 (2016), 722–738
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