Differential-algebraic equations of programmed motions of Lagrangian dynamical systems

Mukharlyamov, R. G.

doi:10.3103/s0025654411040042

Cited by 18 publications

(4 citation statements)

References 1 publication

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“…The development of stable systems of programmed motion and numerical methods for solving differential-algebraic equations is important for the design of anthropoids. Methods for constructing equations of dynamics and solving problems of controlling dynamic systems are proposed in [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. Methods for constructing equations of dynamics, which ensure the stabilization of constraints during numerical solution, and methods for solving problems of controlling the programmed motion of systems for various purposes are described.…”

Section: Main Directions Of the Use Of Exoskeletons In Medicinementioning

confidence: 99%

On Mathematical Modeling of the Dynamics of Multilink Systems and Exoskeletons

Borisov

Kaspirovich

Mukharlyamov

2021

J. Comput. Syst. Sci. Int.

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A review of well-known publications is given and some results of the authors' research on modeling the dynamics of systems of rigid bodies and exoskeletons are presented. Various approaches to the problem of modeling the dynamics of multilink systems are described, including the problems of constructing equations of motion and solving control problems. Matrix and recurrent methods of composing equations for the dynamics of anthropomorphic mechanisms and exoskeletons, as well as problems of modeling flat and spatial systems containing links of variable length, are considered. The results of the research on the analytical design of exoskeletons, anthropomorphic mechanisms, and their analogs seem to be relevant for the design of systems designed to enhance human motor functions and the development of robotic systems for various purposes.

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Section: Main Directions Of the Use Of Exoskeletons In Medicinementioning

confidence: 99%

On Mathematical Modeling of the Dynamics of Multilink Systems and Exoskeletons

Borisov

Kaspirovich

Mukharlyamov

2021

J. Comput. Syst. Sci. Int.

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“…is a system of random processes with independent increments, which, following [19], can be represented as a sum This problem is one of the inverse problems of dynamics, and in the absence of random perturbations ) 0 (   it has been sufficiently fully investigated in [1][2][3][4][5][6], and the case…”

Section: Stochastic Reconstruction Problemmentioning

confidence: 99%

On Inverse Stochastic Reconstruction Problem

Tleubergenov¹,

Vassilina²,

Sarypbek³

2021

News of NAS RK. SPh-M

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In this paper, general reconstruction problem in the class of second-order stochastic differential equations of the Ito type is considered for given properties of motion, when the control is included in the drift coefficient. And the form of control parameters is determined by the quasi-inversion method, which provides necessary and sufficient conditions for existence of a given integral manifold. Further, the solution of the Meshchersky’s stochastic problem is given, which is one of the inverse problems of dynamics and, according to the well-known Galiullin’s classification, refers to the restoration problem. It is assumed that random perturbations belong to the class of processes with independent increments. To solve the posed problem an equation of perturbed motion is drawn up by the Ito rule of stochastic differentiation. And, further, the Erugin method in combination with the quasi-inversion method is used to construct: 1) a set of control vector functions and 2) a set of diffusion matrices that provide necessary and sufficient conditions for a given second-order differential equation of Ito type to have a given integral manifold. The linear case of a stochastic problem with drift control is considered separately. In the linear setting, in contrast to the nonlinear formulation, the conditions of solvability in the presence of random perturbations from the class of processes with independent increments coincide with the conditions of solvability in a similar linear case in the presence of random perturbations from the class of independent Wiener processes. Also considered is the scalar case of the recovery problem with drift controls.

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“…The theory of dynamics inverse problems has been quite fully developed for ordinary differential equations (ODEs) [1][2][3][4][5][6][7][8][9]. This theory goes back to the work by Yerugin [10], in which a set of ODEs is constructed given an integral curve.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Helmholtz problem and convergence in distribution

Tleubergenov

Vassilina

Azhymbaev

2022

Filomat

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In the present paper, the solvability of the stochastic Helmholtz problem is investigated in the class of stochastic differential equations equivalent in distribution. Earlier, by additional variables method the Helmholtz problem was investigated in the class of stochastic differential equations equivalent almost surely (a.s.). The study of the stochastic Helmholtz problem in the class of equations equivalent in distribution allows us to significantly expand the region of its solvability. This is due to the possibility of using well-known methods of the theory of stochastic processes, such as the method of the phase space transformation, the method of absolutely continuous change of measure, and the method of random change of time. In that paper stochastic equations of the Lagrangian structure equivalent in distribution are constructed by the given second order Ito stochastic equations using the methods of phase space transformation, absolutely continuous measure transformation and randomtime substitution. The obtained results are illustrated by specific examples.

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Differential-algebraic equations of programmed motions of Lagrangian dynamical systems

Cited by 18 publications

References 1 publication

On Mathematical Modeling of the Dynamics of Multilink Systems and Exoskeletons

On Mathematical Modeling of the Dynamics of Multilink Systems and Exoskeletons

On Inverse Stochastic Reconstruction Problem

Stochastic Helmholtz problem and convergence in distribution

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