Active change in the state of self-oscillations in machines and mechanisms in a system with various types of nonlinearities of an arbitrary structure under the action of a impulse or harmonic disturbing force

2020 ◽  
pp. 408-414
Author(s):  
B.M. Erlich

The method of actively changing the state of self-oscillations in machines and mechanisms in a system with various types of nonlinearities of an arbitrary structure under the action of external periodic perturbations was proposed. The differential equations of the method take into account two types of external force periodic disturbances: impulse and harmonic.

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1467
Author(s):  
Muminjon Tukhtasinov ◽  
Gafurjan Ibragimov ◽  
Sarvinoz Kuchkarova ◽  
Risman Mat Hasim

A pursuit differential game described by an infinite system of 2-systems is studied in Hilbert space l2. Geometric constraints are imposed on control parameters of pursuer and evader. The purpose of pursuer is to bring the state of the system to the origin of the Hilbert space l2 and the evader tries to prevent this. Differential game is completed if the state of the system reaches the origin of l2. The problem is to find a guaranteed pursuit and evasion times. We give an equation for the guaranteed pursuit time and propose an explicit strategy for the pursuer. Additionally, a guaranteed evasion time is found.


2020 ◽  
Vol 70 (2) ◽  
pp. 401-416
Author(s):  
Hana Machů

Abstract If in the right-hand sides of given differential equations occur discontinuities in the state variables, then the natural notion of a solution is the one in the sense of Filippov. In our paper, we will consider this type of solutions for vector Dirichlet problems. The obtained theorems deal with the existence and localization of Filippov solutions, under effective growth restrictions. Two illustrative examples are supplied.


2020 ◽  
Vol 3 (2) ◽  
pp. 43-47
Author(s):  
Herlin Soraya

In this paper we discuss about how the relationship between non-linear differential equations on aerodynamic damping with linearly viscous damping equations. And it turns out after analyzing that the changes that occur pendulum that changes from the start of the maximum state to a stable state takes time so that changes that occur until the state is stable, this change can be reduced with the use of viscous damper


1863 ◽  
Vol 23 (2) ◽  
pp. 299-348 ◽  
Author(s):  
R. E. Scoresby-Jackson

The subject to which I have to invite the attention of the Society this evening is one of no modern origin, the name of Hippocrates, amongst others of the fathers of medicine, being commonly associated with it. There is, indeed, perhaps no branch of medical inquiry whose history dips more deeply into the obscure pages of antiquity. The influence of weather upon disease and mortality has been acknowledged as a potent external force in every age, from that eminently speculative and credulous period when physicians professed to receive their diagnostic as well as their therapeutic inspirations from the stars, down to our own day. And yet there is perhaps no question in the whole cycle of medical sciences which has made slower progress than the one we have now to consider. People believe that the weather affects them. They speak of its influence, sometimes commendingly, more frequently with censure, on the most trivial occasions; but beyond a few commonplace ideas, the result of careless observation, or perhaps acquired only traditionally, they seldom seek a closer acquaintance with the subject. Our language teems with medico-meteorological apophthegms, but they are notoriously vague. The words which are most commonly employed to signify the state of the weather at any given time, possess a value relative only to the sensations of the individual uttering them. The general and convertible terms—bitter, raw, cold, severe, bleak, inclement, or fine and bracing, convey no definite idea of the condition of the weather; nay, it is quite possible that we may hear these several expressions used by different persons with reference to the weather of one and the same place and point of time. In order, then, to render medico-meteorological researches more trustworthy, we must be careful to employ, in the expression of facts, such symbols only as have a corresponding value in every nation.


2014 ◽  
Vol 12 (2) ◽  
Author(s):  
Alexander Rezounenko

AbstractSystems of differential equations with state-dependent delay are considered. The delay dynamically depends on the state, i.e. is governed by an additional differential equation. By applying the time transformations we arrive to constant delay systems and compare the asymptotic properties of the original and transformed systems.


2010 ◽  
Vol 40-41 ◽  
pp. 27-33 ◽  
Author(s):  
Yi Hui Lin ◽  
Hai Bo Zhang

The method of state space model fitting is carried out by using the linear relation of the variable of the differential equations and separating the steady process and instant process to eliminate the steady errors course by instant errors. The improved fitting method is without solving the linear differential equations or using any iterative methods. The coefficient of the state space model can be solve simply using matrix operation under the premise of high accuracy, so it has a higher computational efficiency than former least square method. And this method can also be used with other fitting method. Finally, to illustrate the validity and accuracy of the improved method, a small perturbation state space model of a certain turboshaft engine model has been established by this method, and the simulation result between state space model and nonlinear model was also compared. Also, the state space model could be applied to fault diagnosis and control system design for aeroengines.


1973 ◽  
Vol 73 (1) ◽  
pp. 119-138 ◽  
Author(s):  
Gerald S. Goodman ◽  
S. Johansen

1. SummaryWe shall consider a non-stationary Markov chain on a countable state space E. The transition probabilities {P(s, t), 0 ≤ s ≤ t <t0 ≤ ∞} are assumed to be continuous in (s, t) uniformly in the state i ε E.


2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Juan J. Nieto ◽  
Rosana Rodríguez-López

We provide optimal conditions for the existence and uniqueness of solutions to a nonlocal boundary value problem for a class of linear homogeneous second-order functional differential equations with piecewise constant arguments. The nonlocal boundary conditions include terms of the state function and the derivative of the state function. A similar nonhomogeneous problem is also discussed.


2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Ezzat G. Bakhoum ◽  
Cristian Toma

This study presents specific aspects of dynamics generated by the coherence function (acting in an integral manner). It is considered that an oscillating system starting to work from initial nonzero conditions is commanded by the coherence function between the output of the system and an alternating function of a certain frequency. For different initial conditions, the evolution of the system is analyzed. The equivalence between integrodifferential equations and integral equations implying the same number of state variables is investigated; it is shown that integro-differential equations of second order are far more restrictive regarding the initial conditions for the state variables. Then, the analysis is extended to equations of evolution where the coherence function is acting under the form of a multiple integral. It is shown that for the coherence function represented under the form of annth integral, some specific aspects as multiscale behaviour suitable for modelling transitions in complex systems (e.g., quantum physics) could be noticed whennequals 4, 5, or 6.


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