On a pendulum motion in multi-dimensional space. Part 3. Dependence of force fields on the tensor of angular velocity
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 24 (2018) no. 2, pp. 33-54
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In the proposed cycle of work, we study the equations of 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 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 this work, we study that case when the force fields linearly depend on the tensor of angular velocity.
Keywords:
multi-dimensional rigid body, non-conservative force field, dynamical system, case of integrability.
@article{VSGU_2018_24_2_a4,
author = {M. V. Shamolin},
title = {On a pendulum motion in multi-dimensional space. {Part} 3. {Dependence} of force fields on the tensor of angular velocity},
journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
pages = {33--54},
publisher = {mathdoc},
volume = {24},
number = {2},
year = {2018},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VSGU_2018_24_2_a4/}
}
TY - JOUR AU - M. V. Shamolin TI - On a pendulum motion in multi-dimensional space. Part 3. Dependence of force fields on the tensor of angular velocity JO - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ PY - 2018 SP - 33 EP - 54 VL - 24 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VSGU_2018_24_2_a4/ LA - ru ID - VSGU_2018_24_2_a4 ER -
%0 Journal Article %A M. V. Shamolin %T On a pendulum motion in multi-dimensional space. Part 3. Dependence of force fields on the tensor of angular velocity %J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ %D 2018 %P 33-54 %V 24 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/VSGU_2018_24_2_a4/ %G ru %F VSGU_2018_24_2_a4
M. V. Shamolin. On a pendulum motion in multi-dimensional space. Part 3. Dependence of force fields on the tensor of angular velocity. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 24 (2018) no. 2, pp. 33-54. http://geodesic.mathdoc.fr/item/VSGU_2018_24_2_a4/