Vestnik SamU. Estestvenno-Nauchnaya Ser., 2017, Issue 3, Pages 41–64
On a pendulum motion in multi-dimensional space. Part 1. Dynamical systems
M. V. Shamolin
Institute of Mechanics, Lomonosov Moscow
State University, Moscow, 119192, Russian Federation
In the proposed cycle of work, we study the equations of the motion of dynamically symmetric fixed $n$-dimensional rigid bodies-pendulums located in a nonconservative force fields. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of a medium. In parallel, we study the problem of the motion of a free $n$-dimensional rigid body also located in a similar force fields. Herewith, this free rigid body is influenced by a nonconservative tracing force; under action of this force, either the magnitude of the velocity of some characteristic point of the body remains constant, which means that the system possesses a nonintegrable servo constraint. In thit work, we derive the general multi-dimensional dynamic equations of the systems under study.
multi-dimensional rigid body, non-conservative force field, dynamical system, case of integrability.
|Russian Foundation for Basic Research
|The work is carried out at the financial support of the grant of the Russian Foundation for Basic Research 15-01-00848-a.
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M. V. Shamolin, “On a pendulum motion in multi-dimensional space. Part 1. Dynamical systems”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 2017, no. 3, 41–64
Citation in format AMSBIB
\paper On a pendulum motion in multi-dimensional space. Part 1. Dynamical systems
\jour Vestnik SamU. Estestvenno-Nauchnaya Ser.
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