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A Survey of Starzhinskii's Works on Stability of Periodic Motions and Nonlinear Oscillations*
Published in A.A. Martynyuk, Advances in Stability Theory at the End of the 20th Century, 2002
Yu.A. Mitropol'skii, A.A. Martynyuk, V.I. Zhukovskii
H1(l) is the matrix coefficient of the Fourier series H1(ϑz)∼ΣeiλϑzH1(λ);
Low-Frequency Near-Field Magnetic Scattering From Highly, but not Perfectly, Conducting Bodies
Published in Carl E. Baum, Detection and Identification of Visually Obscured Targets, 2019
More generally one can invert the matrix coefficient and solve for the numerical current vector as a matrix times (dot product) the numerical voltage vector. This matrix has elements which are ratios of polynomials in s. This fact alone, however, is not sufficient to exclude second- and higher-order poles, nor to give only real natural frequencies. There is, however, the canonical example of the sphere in [25,28] and Appendix 6E, as well as practical experience [29] to indicate that the natural frequencies are real and the poles are first order, at least for some cases of interest.
Filtering and Extrapolation of Target Track Parameters Based on Radar Measure
Published in Vyacheslav Tuzlukov, Signal Processing in Radar Systems, 2017
The matrix coefficient of filter amplification defined as Gn=ΨnHnTRn−1
Analytical method for free-damped vibration analysis of viscoelastic shear deformable annular plates made of functionally graded materials
Published in Mechanics Based Design of Structures and Machines, 2019
Seyed Hashem Alavi, Hamidreza Eipakchi
For a nontrivial solution, the determinant of the matrix coefficient must be vanished which is known as the dispersion equation. By solving Eq. (16b), six eigenvalues sm (m = 1.6) are obtained which are functions of ω. is the eigenvector corresponds to the eigenvalue sm. So, the total solution (Eq. 15) are determined. By applying the boundary conditions, one set of homogenous algebraic equation [b]{dm(T1)} = {0};m = 1.6 is derived. For nonzero solution, the determinant of the coefficient matrix [b] is equated to zero and it result one complicated algebraic equation in terms of ω. The root of this equation is the dimensionless frequency. In this case, d1(T1), d2(T1), d3(T1), d4(T1), d5(T1) are calculated in terms of d6(T1).
Reinforcement learning based compliance control of a robotic walk assist device
Published in Advanced Robotics, 2019
S. G. Khan, M. Tufail, S. H. Shah, I. Ullah
Both hip and knee joints are made to follow the behavior of a second order mass-spring-damper system. As mentioned above, the main idea is to mimic the compliant behavior of a model inertia, rotational spring-damper system. In addition, this may be helpful in the rehabilitation of the user. For example, if human is gaining strength and starts applying more efforts, then RWAD will reduce the amount of applied torque. The compliant, reference model (Figures 3 and 4) is defined by the inertia matrix , the damping matrix coefficient and the stiffness coefficient matrix . These values determine the behavior of the reference model [40–43], where is the sensed torques vector , is the reference trajectory vector(hip and knee joints) and is a the new reference position vector to compensate the human effort (interaction torque, sensed in the torque sensors in hip and knee joints). Therefore, , and can be employed to tune the level of compliance, e.g. if is decreased, the robot becomes more compliant. In this paper, all these values are manually selected. However, this a potential future work to learn suitable compliance levels.
Out-of-plane compression failure calculation for self-lubricating fabric liner based on progressive damage theory
Published in The Journal of The Textile Institute, 2022
Jigang Chen, Xiaokang Wang, Qiang Zhang, Guanghui Yang, Yahong Xue
Thus, the constitutive relationship equation of fiber bundles with damage variables is: 2. For isotropic resin matrix materials, the values of the damage variables are the same, that is, Thus, the stiffness matrix coefficient of matrix can be calculated as: