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Статті в журналах з теми "Dynamical Inverse Problem"

Автор: Grafiati

Опубліковано: 11 березня 2023

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1

Khan, B. A., S. Chatterjee, S. G. Ali, and B. Talukdar. "Inverse Variational Problem for Nonlinear Dynamical Systems." Acta Physica Polonica A 141, no. 1 (January 2022): 64–73. http://dx.doi.org/10.12693/aphyspola.141.64.

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2

MORASSI, A., G. NAKAMURA, and M. SINI. "An inverse dynamical problem for connected beams." European Journal of Applied Mathematics 16, no. 1 (March 23, 2005): 83–109. http://dx.doi.org/10.1017/s0956792505005826.

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3

Avdonin, S. A., B. P. Belinskiy, and J. V. Matthews. "Dynamical inverse problem on a metric tree." Inverse Problems 27, no. 7 (June 14, 2011): 075011. http://dx.doi.org/10.1088/0266-5611/27/7/075011.

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4

Merritt, David. "The Dynamical Inverse Problem for Axisymmetric Stellar Systems." Astronomical Journal 112 (September 1996): 1085. http://dx.doi.org/10.1086/118080.

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5

Belishev, M. I. "Dynamical inverse problem for a Lamé type system." Journal of Inverse and Ill-posed Problems 14, no. 8 (December 2006): 751–66. http://dx.doi.org/10.1515/156939406779768300.

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6

Kharchenko, N. V. "Inverse problem of spectral analysis of conflict dynamical systems." Ukrainian Mathematical Journal 62, no. 1 (August 2010): 123–35. http://dx.doi.org/10.1007/s11253-010-0337-3.

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7

Baev, A. V. "Solution of the inverse dynamical seismic problem with absorption." Computational Mathematics and Modeling 4, no. 2 (1993): 122–24. http://dx.doi.org/10.1007/bf01131204.

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8

Federico, Salvatore, and Mawafag Alhasadi. "Inverse dynamics in rigid body mechanics." Theoretical and Applied Mechanics, no. 00 (2022): 11. http://dx.doi.org/10.2298/tam221109011f.

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Анотація:

Inverse Dynamics is used to calculate the forces and moments in the joints of multibody systems investigated in fields such as Biomechanics or Robotics. In a didactic spirit, this paper begins with an overview of the derivations of the kinematical and dynamical equations of rigid bodies from the point of view of modern Continuum Mechanics. Then, it introduces a matrix formulation for the solution of Inverse Dynamics problems and, finally, reports a simple two-dimensional example of application to a problem in Biomechanics.

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9

Chu, Moody T., and Gene H. Golub. "Structured inverse eigenvalue problems." Acta Numerica 11 (January 2002): 1–71. http://dx.doi.org/10.1017/s0962492902000016.

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Анотація:

An inverse eigenvalue problem concerns the reconstruction of a structured matrix from prescribed spectral data. Such an inverse problem arises in many applications where parameters of a certain physical system are to be determined from the knowledge or expectation of its dynamical behaviour. Spectral information is entailed because the dynamical behaviour is often governed by the underlying natural frequencies and normal modes. Structural stipulation is designated because the physical system is often subject to some feasibility constraints. The spectral data involved may consist of complete or only partial information on eigenvalues or eigenvectors. The structure embodied by the matrices can take many forms. The objective of an inverse eigenvalue problem is to construct a matrix that maintains both the specific structure as well as the given spectral property. In this expository paper the emphasis is to provide an overview of the vast scope of this intriguing problem, treating some of its many applications, its mathematical properties, and a variety of numerical techniques.

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10

Mikhaylov, Alexander, and Victor Mikhaylov. "Inverse problem for dynamical system associated with Jacobi matrices and classical moment problems." Journal of Mathematical Analysis and Applications 487, no. 1 (July 2020): 123970. http://dx.doi.org/10.1016/j.jmaa.2020.123970.

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11

Demchenko, M. N. "The dynamical 3-dimensional inverse problem for the Maxwell system." St. Petersburg Mathematical Journal 23, no. 6 (September 17, 2012): 943–75. http://dx.doi.org/10.1090/s1061-0022-2012-01224-0.

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12

Morassi, Antonino, Gen Nakamura, Kenji Shirota, and Mourad Sini. "Numerical method for an inverse dynamical problem for composite beams." Journal of Physics: Conference Series 73 (June 1, 2007): 012015. http://dx.doi.org/10.1088/1742-6596/73/1/012015.

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13

Omarova, G. T., and T. S. Kozhanov. "Application of Szebehely’s Inverse Problem to Non-Stationary Dynamical Systems." International Astronomical Union Colloquium 132 (1993): 373–77. http://dx.doi.org/10.1017/s0252921100066264.

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AbstractA first-order linear partial differential equation is presented, giving the non-stationary potential functions U=U (x,y,t) which give rise to a given family of evoling planar orbits f(x,y,t) = c in two-dimensional dynamical system. It is shown, that this equation is applied in celestial mechanics of variable mass.

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14

Zamparo, M., S. Stramaglia, J. R. Banavar, and A. Maritan. "Inverse problem for multivariate time series using dynamical latent variables." Physica A: Statistical Mechanics and its Applications 391, no. 11 (June 2012): 3159–69. http://dx.doi.org/10.1016/j.physa.2012.01.037.

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15

Bellassoued, Mourad, Michel Cristofol, and Eric Soccorsi. "Inverse boundary value problem for the dynamical heterogeneous Maxwell's system." Inverse Problems 28, no. 9 (August 23, 2012): 095009. http://dx.doi.org/10.1088/0266-5611/28/9/095009.

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16

Slodička, M. "A parabolic inverse source problem with a dynamical boundary condition." Applied Mathematics and Computation 256 (April 2015): 529–39. http://dx.doi.org/10.1016/j.amc.2015.01.103.

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17

Esquivel, Ricardo Medel, Isidro Gómez-Vargas, Teodoro Rivera Montalvo, J. Alberto Vázquez, and Ricardo García-Salcedo. "The inverse problem of a dynamical system solved with genetic algorithms." Journal of Physics: Conference Series 1723, no. 1 (January 1, 2021): 012021. http://dx.doi.org/10.1088/1742-6596/1723/1/012021.

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18

Caviglia, G. "Dynamical symmetries, first integrals and the inverse problem of Lagrangian dynamics." Inverse Problems 1, no. 2 (May 1, 1985): L13—L17. http://dx.doi.org/10.1088/0266-5611/1/2/002.

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19

MORASSI, ANTONIO, GEN NAKAMURA, KENJI SHIROTA, and MOURAD SINI. "A variational approach for an inverse dynamical problem for composite beams." European Journal of Applied Mathematics 18, no. 1 (February 2007): 21–55. http://dx.doi.org/10.1017/s0956792507006833.

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Анотація:

This paper deals with a problem of nondestructive testing for a composite system formed by the connection of a steel beam and a reinforced concrete beam. The small vibrations of the composite beam are described by a differential system where a coupling takes place between longitudinal and bending motions. The motion is governed in space by two second order and two fourth order differential operators, which are coupled in the lower order terms by the shearing,k, and axial, μ, stiffness coefficients of the connection. The coefficientskand μ define the mechanical model of the connection between the steel beam and the concrete beam and contain direct information on the integrity of the system. In this paper we study the inverse problem of determiningkand μ by mixed data. The inverse problem is transformed to a variational problem for a cost function which includes boundary measurements of Neumann data and also some interior measurements. By computing the Gateaux derivatives of the functional, an algorithm based on the projected gradient method is proposed for identifying the unknown coefficients. The results of some numerical simulations on real steel-concrete beams are presented and discussed.

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20

Belishev, M. I., and N. A. Karazeeva. "Simplest Test for the Two-Dimensional Dynamical Inverse Problem (BC-Method)." Journal of Mathematical Sciences 243, no. 5 (November 14, 2019): 656–70. http://dx.doi.org/10.1007/s10958-019-04567-5.

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21

Belishev, M. I., and V. S. Mikhailov. "Inverse problem for a one-dimensional dynamical Dirac system (BC-method)." Inverse Problems 30, no. 12 (December 1, 2014): 125013. http://dx.doi.org/10.1088/0266-5611/30/12/125013.

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22

Isakov, Victor, Jenn-Nan Wang, and Masahiro Yamamoto. "An Inverse Problem for a Dynamical Lamé System with Residual Stress." SIAM Journal on Mathematical Analysis 39, no. 4 (January 2008): 1328–43. http://dx.doi.org/10.1137/060669115.

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23

Salahshour, Soheil, Ali Ahmadian, Bruno A. Pansera, and Massimiliano Ferrara. "Uncertain inverse problem for fractional dynamical systems using perturbed collage theorem." Communications in Nonlinear Science and Numerical Simulation 94 (March 2021): 105553. http://dx.doi.org/10.1016/j.cnsns.2020.105553.

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24

Zaika, Yury V., Natalia I. Rodchenkova, and Ekaterina K. Kostikova. "The Inverse Problem of Identification of Hydrogen Permeability Model." Advances in Mathematical Physics 2018 (June 7, 2018): 1–19. http://dx.doi.org/10.1155/2018/4628346.

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Анотація:

One of the technological challenges for hydrogen materials science is the currently active search for structural materials with important applications (including the ITER project and gas-separation plants). One had to estimate the parameters of diffusion and sorption to numerically model the different scenarios and experimental conditions of the material usage (including extreme ones). The article presents boundary value problems of hydrogen permeability and thermal desorption with dynamical boundary conditions. A numerical method is developed for TDS spectrum simulation, where only integration of a nonlinear system of low order ordinary differential equations is required. The main final output of the article is a noise-resistant algorithm for solving the inverse problem of parametric identification for the aggregated experiment where desorption and diffusion are dynamically interrelated (without the artificial division of studies into the diffusion limited regime (DLR) and the surface limited regime (SLR)).

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25

Niven, Robert, Ali Mohammad-Djafari, Laurent Cordier, Markus Abel, and Markus Quade. "Bayesian Identification of Dynamical Systems." Proceedings 33, no. 1 (February 12, 2020): 33. http://dx.doi.org/10.3390/proceedings2019033033.

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Анотація:

Many inference problems relate to a dynamical system, as represented by dx/dt = f (x), where x ∈ ℝn is the state vector and f is the (in general nonlinear) system function or model. Since the time of Newton, researchers have pondered the problem of system identification: how should the user accurately and efficiently identify the model f – including its functional family or parameter values – from discrete time-series data? For linear models, many methods are available including linear regression, the Kalman filter and autoregressive moving averages. For nonlinear models, an assortment of machine learning tools have been developed in recent years, usually based on neural network methods, or various classification or order reduction schemes. The first group, while very useful, provide “black box" solutions which are not readily adaptable to new situations, while the second group necessarily involve the sacrificing of resolution to achieve order reduction. To address this problem, we propose the use of an inverse Bayesian method for system identification from time-series data. For a system represented by a set of basis functions, this is shown to be mathematically identical to Tikhonov regularization, albeit with a clear theoretical justification for the residual and regularization terms, respectively as the negative logarithms of the likelihood and prior functions. This insight justifies the choice of regularization method, and can also be extended to access the full apparatus of the Bayesian inverse solution. Two Bayesian methods, based on the joint maximum a posteriori (JMAP) and variational Bayesian approximation (VBA), are demonstrated for the Lorenz equation system with added Gaussian noise, in comparison to the regularization method of least squares regression with thresholding (the SINDy algorithm). The Bayesian methods are also used to estimate the variances of the inferred parameters, thereby giving the estimated model error, providing an important advantage of the Bayesian approach over traditional regularization methods.

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26

Bellassoued, Mourad, and Imen Rassas. "Stability estimate for an inverse problem of the convection-diffusion equation." Journal of Inverse and Ill-posed Problems 28, no. 1 (February 1, 2020): 71–92. http://dx.doi.org/10.1515/jiip-2018-0072.

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AbstractWe consider the inverse boundary value problem for the dynamical steady-state convection-diffusion equation. We prove that the first-order coefficient and the scalar potential are uniquely determined by the Dirichlet-to-Neumann map. More precisely, we show in dimension {n\geq 3} a log-type stability estimate for the inverse problem under consideration. The method is based on reducing our problem to an auxiliary inverse problem and the construction of complex geometrical optics solutions of this problem.

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27

Banerjee, B., D. Roy, and R. M. Vasu. "A pseudo-dynamical systems approach to a class of inverse problems in engineering." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2105 (February 25, 2009): 1561–79. http://dx.doi.org/10.1098/rspa.2008.0501.

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Анотація:

A pseudo-dynamical approach for a class of inverse problems involving static measurements is proposed and explored. Following linearization of the minimizing functional associated with the underlying optimization problem, the new strategy results in a system of linearized ordinary differential equations (ODEs) whose steady-state solutions yield the desired reconstruction. We consider some explicit and implicit schemes for integrating the ODEs and thus establish a deterministic reconstruction strategy without an explicit use of regularization. A stochastic reconstruction strategy is then developed making use of an ensemble Kalman filter wherein these ODEs serve as the measurement model. Finally, we assess the numerical efficacy of the developed tools against a few linear and nonlinear inverse problems of engineering interest.

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28

Johnson, C. D. "New results on the inverse-system/deconvolution problem for linear dynamical systems." Circuits Systems and Signal Processing 19, no. 4 (July 2000): 365–83. http://dx.doi.org/10.1007/bf01200893.

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29

Pestov, A. L. "On an Inverse Problem for a One-Dimensional Two-Velocity Dynamical System." Journal of Mathematical Sciences 214, no. 3 (March 11, 2016): 344–71. http://dx.doi.org/10.1007/s10958-016-2782-5.

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30

Fomenko, V. G. "The Dynamical Inverse Problem for a Lamé Type System (The BC Method)." Journal of Mathematical Sciences 214, no. 3 (March 11, 2016): 392–421. http://dx.doi.org/10.1007/s10958-016-2785-2.

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31

Perkins, Theodore J., Mike Hallett, and Leon Glass. "Dynamical properties of model gene networks and implications for the inverse problem." Biosystems 84, no. 2 (May 2006): 115–23. http://dx.doi.org/10.1016/j.biosystems.2005.09.010.

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32

Avdonin, S. A., M. I. Belishev, and Yu S. Rozhkov. "The dynamical inverse problem for a non-self-adjoint sturm-liouville operator." Journal of Mathematical Sciences 102, no. 4 (December 2000): 4139–48. http://dx.doi.org/10.1007/bf02673844.

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33

Bevilacqua, Luiz, and Marcelo M. Barros. "The inverse problem for fractal curves solved with the dynamical approach method." Chaos, Solitons & Fractals 168 (March 2023): 113113. http://dx.doi.org/10.1016/j.chaos.2023.113113.

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34

CYRIL, X., J. ANGELES, and A. MISRA. "EFFICIENT INVERSE DYNAMICS OF GENERAL N-AXIS ROBOTIC MANIPULATORS." Transactions of the Canadian Society for Mechanical Engineering 13, no. 4 (December 1989): 91–95. http://dx.doi.org/10.1139/tcsme-1989-0015.

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Анотація:

Presented in this paper is an efficient scheme to solve the inverse dynamics problem associated with robotic manipulators of arbitrary architecture, using the recursive Newton-Euler formulation. The scheme’s efficiency derives from the use of suitable coordinate frame to represent the vector quantities and the suitable manipulation of the vector operations. The computational complexities of this and other general dynamical formulations published so far are compared. In conclusion, it is observed that not only the dynamical formulation methodology, but also the judicious representation and manipulation of the vector quantities contribute to the computational efficiency of the algorithm. An example is presented to show the validity of the computational scheme.

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35

Bratchikiov, D. S., and K. G. Gadylshin. "Solution of an inverse dynamical seismic problem on the base of a deep convolutional neural network." Interexpo GEO-Siberia 2, no. 2 (May 18, 2022): 292–304. http://dx.doi.org/10.33764/2618-981x-2022-2-2-292-304.

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Анотація:

The paper presents an original approach to solving the inverse dynamical seismic problem for the scalar wave equation in seismic monitoring. Instead of using the expensive full waveform inversion method, it is proposed to approximate the inverse problem operator, which translates the difference in the data into the models' perturbation, using a deep convolutional neural network of the Unet type architecture. The operability of this approach was demonstrated on a simple test example.

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36

Mikhaylov, Alexander, and Victor Mikhaylov. "Inverse problems for finite Jacobi matrices and Krein–Stieltjes strings." Journal of Inverse and Ill-posed Problems 29, no. 4 (April 2, 2021): 611–28. http://dx.doi.org/10.1515/jiip-2020-0112.

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Abstract We consider dynamic inverse problems for a dynamical system associated with a finite Jacobi matrix and for a system describing propagation of waves in a finite Krein–Stieltjes string. We offer three methods of recovering unknown parameters: entries of a Jacobi matrix in the first problem and point masses and distances between them in the second, from dynamic Dirichlet-to-Neumann operators. We also answer a question on a characterization of dynamic inverse data for these two problems.

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37

Xu, He Long, Jun Xiao, and Yu Xin Zhang. "Dynamical Model Updating Based on Gradient Regularization Method." Applied Mechanics and Materials 351-352 (August 2013): 118–21. http://dx.doi.org/10.4028/www.scientific.net/amm.351-352.118.

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Modulus of elasticity is an important input parameter in all kinds of structural analyses. The mathematical model used to identify the structural elastic modulus with measured Frequencies and mode shapes at several points is thusly built up in this paper, and then Gradient-Regularization method, an inverse problem solution method, is employed to solve the problem. General finite element program is compiled, and numerical examples have proved that the method of this thesis is efficient. The issues such as the choice of model error and the choice of measuring points are discussed as well.

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38

Лосанова, Ф. М. "Inverse problem for McKendrick von Foerster equation with Caputo operator." Вестник КРАУНЦ. Физико-математические науки, no. 3 (December 5, 2022): 111–18. http://dx.doi.org/10.26117/2079-6641-2022-40-3-111-118.

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Анотація:

Операторы дробного интегро-дифференцирования широко применяются при исследовании прикладных задач, изучающих математические модели физических и геофизических процессов во фрактальных средах. Производная дробного порядка не является локальной, что демонстрирует поведение с долговременной памятью. Благодаря этому, модели динамических систем дробного порядка более точные, чем целочисленные. В данной работе рассматривается обратная задача для обобщенной математической модели биологического процесса, характеризующей динамику численности популяции с возрастной структурой. Обобщение определяется введением в уравнение производной дробного порядка в смысле Капуто. Fractional integro-differentiation operators are widely used in the study of applied problems that study mathematical models of physical and geophysical processes in fractal media. The fractional order derivative is not local, which exhibits behavior with long-term memory. Due to this, the models of dynamical systems of fractional order are more accurate than integer ones. In this paper, we consider an inverse problem for a generalized mathematical model of a biological process that characterizes the dynamics of a population with an age structure. The generalization is defined by introducing a derivative of a fractional order in the sense of Caputo into the equation.

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39

Belishev, M. I., and A. L. Pestov. "Characterization of the inverse problem data for one-dimensional two-velocity dynamical system." St. Petersburg Mathematical Journal 26, no. 3 (March 20, 2015): 411–40. http://dx.doi.org/10.1090/s1061-0022-2015-01344-7.

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40

Ikehata, Masaru. "An inverse acoustic scattering problem inside a cavity with dynamical back-scattering data." Inverse Problems 28, no. 9 (August 29, 2012): 095016. http://dx.doi.org/10.1088/0266-5611/28/9/095016.

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41

Cariñena, José F., and José Fernández-Núñez. "Jacobi Multipliers in Integrability and the Inverse Problem of Mechanics." Symmetry 13, no. 8 (August 2, 2021): 1413. http://dx.doi.org/10.3390/sym13081413.

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Анотація:

We review the general theory of the Jacobi last multipliers in geometric terms and then apply the theory to different problems in integrability and the inverse problem for one-dimensional mechanical systems. Within this unified framework, we derive the explicit form of a Lagrangian obtained by several authors for a given dynamical system in terms of known constants of the motion via a Jacobi multiplier for both autonomous and nonautonomous systems, and some examples are used to illustrate the general theory. Finally, some geometric results on Jacobi multipliers and their use in the study of Hojman symmetry are given.

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42

Dariush, Behzad, Hooshang Hemami, and Mohamad Parnianpour. "Multi-Modal Analysis of Human Motion From External Measurements." Journal of Dynamic Systems, Measurement, and Control 123, no. 2 (February 1, 2001): 272–78. http://dx.doi.org/10.1115/1.1370375.

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Анотація:

The “analysis” or “inverse dynamics” problem in human motion studies assumes knowledge of the motion of the dynamical system in various forms and/or measurements of ground reaction forces to determine the applied forces and moments at the joints. Conceptually, methods of attacking such problems are well developed and satisfactory solutions have been obtained if the input signals are noise free and the dynamic model is perfect. In this ideal case, an inverse solution exists, is unique, and depends continuously on the initial data. However, the inverse solution may require the calculation of higher order derivatives of experimental observations contaminated by noise—a notoriously difficult problem. The byproduct of errors due to numerical differentiation is grossly erroneous joint force and moment calculations. This paper provides a framework for analyzing human motion for different sensing conditions in a manner that avoids or minimizes the number of derivative computations. In particular, two sensing modalities are considered: 1) image based and 2) multi-modal sensing: combining imaging, force plate, and accelerometery.

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43

Xiong, Qiao, and Han Bin Xiao. "Inverse Kinematics and Dynamics Simulation of a Dredging Clamshell." Applied Mechanics and Materials 364 (August 2013): 107–11. http://dx.doi.org/10.4028/www.scientific.net/amm.364.107.

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Анотація:

This paper proposes a problem of flat dredging because of the phenomenon of overdredging casuing bottom roughness in dredging engineering and presents the formulation of the inverse kinematics and dynamics simulation of a dredging clamshell. A dynamical model of dredging clamshell is built based on Adams and the position analysis is firstly performed by adding a general point motion to the dredging clamshell. By analyzing and solving kinematics equations in inverse, movement curves of the steel wire ropes are obtained, and the pulling force curves are acquired by dynamics simulation. The results show that the method automatically generates inverse dynamic solutions and the movement curves are intuitive and can offer help to the flat dredging control scheme effectively.

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44

Li, Mimi, Gongsheng Li, Zhiyuan Li, and Xianzheng Jia. "Determination of Time-Dependent Coefficients in Time-Fractional Diffusion Equations by Variational Iteration Method." Journal of Mathematics Research 12, no. 1 (January 31, 2020): 74. http://dx.doi.org/10.5539/jmr.v12n1p74.

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Анотація:

Inverse problems of determining time-dependent coefficients in partial differential equations are difficult to deal with in general cases. The variational iteration method is introduced to determine the time-dependent coefficient in the fractional diffusion equation as well as the solution of the forward problem. By utilizing the additional condition and the property of the fractional derivative, an expression of the unknown is derived by which a nonlinear dynamical differential equation is obtained. The variational iteration method is applied to solve the nonlinear system and the time-dependent coefficient can be reconstructed in a semi-analytical form. Such method can give explicit expression of the solution in the meaning of approximation, or exact solution to the inverse problem in some cases. Several examples are presented to demonstrate feasibility and effectiveness of the proposed method for inverse time-dependent coefficient problems in the fractional diffusion equations.

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45

Li, Mimi, Gongsheng Li, Zhiyuan Li, and Xianzheng Jia. "Determination of Time-Dependent Coefficients in Time-Fractional Diffusion Equations by Variational Iteration Method." Journal of Mathematics Research 12, no. 1 (January 31, 2020): 82. http://dx.doi.org/10.5539/jmr.v12n1p82.

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Анотація:

Inverse problems of determining time-dependent coefficients in partial differential equations are difficult to deal with in general cases. The variational iteration method is introduced to determine the time-dependent coefficient in the fractional diffusion equation as well as the solution of the forward problem. By utilizing the additional condition and the property of the fractional derivative, an expression of the unknown is derived by which a nonlinear dynamical differential equation is obtained. The variational iteration method is applied to solve the nonlinear system and the time-dependent coefficient can be reconstructed in a semi-analytical form. Such method can give explicit expression of the solution in the meaning of approximation, or exact solution to the inverse problem in some cases. Several examples are presented to demonstrate feasibility and effectiveness of the proposed method for inverse time-dependent coefficient problems in the fractional diffusion equations.

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46

Kabanikhin, Sergey I., Nikita S. Novikov, and Maxim A. Shishlenin. "Gelfand-Levitan-Krein method in one-dimensional elasticity inverse problem." Journal of Physics: Conference Series 2092, no. 1 (December 1, 2021): 012022. http://dx.doi.org/10.1088/1742-6596/2092/1/012022.

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Анотація:

Abstract In this article we propose the numerical solution of the one dimensional inverse coefficient problem for seismic equation. We use a dynamical version of Gelfand-Levitan-Krein approach for reducing a nonlinear inverse problem for recovering the shear wave’s velocity and the density of the medium to two sequences of the linear integral equations. We propose numerical algorithm for solving these equations based on a fast inversion of a Toeplitz matrix. The proposed numerical methods base on the structure of the problem and therefore improve the efficiency of the algorithms, compared with standard approaches. We present numerical results for solving considered integral equations.

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47

BOLLT, ERIK M. "CONTROLLING CHAOS AND THE INVERSE FROBENIUS–PERRON PROBLEM: GLOBAL STABILIZATION OF ARBITRARY INVARIANT MEASURES." International Journal of Bifurcation and Chaos 10, no. 05 (May 2000): 1033–50. http://dx.doi.org/10.1142/s0218127400000736.

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Анотація:

The inverse Frobenius–Perron problem (IFPP) is a global open-loop strategy to control chaos. The goal of our IFPP is to design a dynamical system in ℜn which is: (1) nearby the original dynamical system, and (2) has a desired invariant density. We reduce the question of stabilizing an arbitrary invariant measure, to the question of a hyperplane intersecting a unit hyperbox; several controllability theorems follow. We present a generalization of Baker maps with an arbitrary grammar and whose FP operator is the required stochastic matrix.

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48

Stanhope, S., J. E. Rubin, and D. Swigon. "Robustness of Solutions of the Inverse Problem for Linear Dynamical Systems with Uncertain Data." SIAM/ASA Journal on Uncertainty Quantification 5, no. 1 (January 2017): 572–97. http://dx.doi.org/10.1137/16m1062466.

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49

Avdonin, Sergei, Suzanne Lenhart, and Vladimir Protopopescu. "Solving the dynamical inverse problem for the Schrödinger equation by the boundary control method." Inverse Problems 18, no. 2 (February 25, 2002): 349–61. http://dx.doi.org/10.1088/0266-5611/18/2/304.

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50

Galka, Andreas, Okito Yamashita, Tohru Ozaki, Rolando Biscay, and Pedro Valdés-Sosa. "A solution to the dynamical inverse problem of EEG generation using spatiotemporal Kalman filtering." NeuroImage 23, no. 2 (October 2004): 435–53. http://dx.doi.org/10.1016/j.neuroimage.2004.02.022.

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