Levi-Civita symbols, generalized vector products, and new integrable cases in mechanics of multidimensional bodies

DOI10.1007/s10958-012-1065-zzbMath1278.70007OpenAlexW2058007284MaRDI QIDQ1948587

M. V. Shamolin, D. V. Georgievskii

Publication date: 24 April 2013

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-012-1065-z

zbMATH Keywords

dynamics of a rigid bodyintegrable motion

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Integrable cases of motion in rigid body dynamics (70E40) Higher-dimensional generalizations in rigid body dynamics (70E45)

Related Items (11)

Integrable cases in the dynamics of a multi-dimensional rigid body in a nonconservative field in the presence of a tracking force ⋮ New cases of integrability of equations of motion of a rigid body in the \(n\)-dimensional space ⋮ Constitutive relations in multidimensional isotropic elasticity and their restrictions to subspaces of lower dimensions ⋮ Classification of integrable cases in the dynamics of a four-dimensional rigid body in a nonconservative field in the presence of a tracking force ⋮ Performance of an XXX Heisenberg model-based quantum heat engine and tripartite entanglement ⋮ Integrable variable dissipation systems on the tangent bundle of a multi-dimensional sphere and some applications ⋮ Generalized compatibility equations for tensors of high ranks in multidimensional continuum mechanics ⋮ Low-dimensional and multidimensional pendulums in nonconservative fields. I ⋮ Low-dimensional and multidimensional pendulums in nonconservative fields. II ⋮ On the compatibility equations in terms of stresses in many-dimensional elastic medium ⋮ Variety of integrable cases in dynamics of low- and multi-dimensional rigid bodies in nonconservative force fields

Cites Work

• Equivalence of formulations for problems in elasticity theory in terms of stresses
• On the proof of the \(\Pi\)-Theorem in dimension theory
• Body motion in a resisting medium
• New integrable, in the sense of Jacobi, cases in the dynamics of a rigid body interacting with a medium.
• The number of independent compatibility equations in the mechanics of deformable solids
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