Geodesic
Reduction of mathematical model of robot with elastic joints
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 3 (2014), pp. 20-33

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A model of $n$-joint manipulator with elastic joints with small dissipation is studied. Class of singularly perturbed differential systems that describe the dynamics of robot is singled out. For a given class of systems the existence and uniqueness of integral manifoldness of slow movement is established, its features are studied. It is proved that integral manifold may be constructed with any degree of accuracy as asymptotic decomposition in powers of small parameter. System that is used to describe movement in manifolds may be used as a reduced model of initial system.
Keywords: singularly perturbed systems, integral manifolds, asymptotic methods, reduction. 
@article{VSGU_2014_3_a1,
     author = {O. V. Vidilina and N. V. Voropaeva},
     title = {Reduction of mathematical model of robot with elastic joints},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {20--33},
     publisher = {mathdoc},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2014_3_a1/}
}
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O. V. Vidilina; N. V. Voropaeva. Reduction of mathematical model of robot with elastic joints. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 3 (2014), pp. 20-33. http://geodesic.mathdoc.fr/item/VSGU_2014_3_a1/