To ensure the maneuvering capabilities of aircraft and high-speed sea vessels, designers should k... more To ensure the maneuvering capabilities of aircraft and high-speed sea vessels, designers should know the moments of inertia of their massive parts. But since the structure of some elements such as power units is very complicated, it is impossible to determine their moments of inertia analytically. Thus the problem of measuring the moments of inertia of massive large bodies arises.
A linear oscillator with limited excitation force (control function) is under consideration. The ... more A linear oscillator with limited excitation force (control function) is under consideration. The optimal control, which brings oscillatory system to a certain energy level from any initial conditions at the minimal time, is found. The synthesis of control is done. Multi-dimensional case is also studied. The problem has mechanical application to inertia moments measuring by oscillations of a rigid body in elastic support with several degrees of freedom.
Trudy ordena Lenina Matematičeskogo instituta im. V.A. Steklova, Nov 30, 2021
<jats:p>Оптимизируется сбор возобновляемого ресурса, распределенного на окружности. Динамик... more <jats:p>Оптимизируется сбор возобновляемого ресурса, распределенного на окружности. Динамика восстановления ресурса описывается уравнением типа Колмогорова-Петровского-Пискунова-Фишера в дивергентной форме, а сбор ресурса осуществляется движущейся циклически по окружности машиной, при этом в функционале качества учитываются положение этой машины, сложность обнаружения или сбора ресурса из этого положения, а также удаление ресурса от него. Доказано существование оптимального движения собирающей машины, доставляющего максимум средней временно́й выгоды в натуральном виде в долгосрочной перспективе при начальном распределении ресурса, не меньшем предельного при отсутствии сбора.</jats:p>
We analyze the effects of anticipated population aging within a general equilibrium R&D-based end... more We analyze the effects of anticipated population aging within a general equilibrium R&D-based endogenous growth model with overlapping generations. In doing so we model aging as a rise of longevity and a simultaneous drop in fertility. In contrast to an unanticipated rise of longevity, consumers increase their savings and reduce their consumption long before the rise of longevity actually happens. This implies that individuals save more in anticipation of aging, which puts downward pressure on the interest rate and raises economic growth through an increase in R&D incentives. Irrespective of the anticipation effect, the economic change at impact is not smooth but still features a kink in consumption.
where u(t) ∈ U and x(t) ∈ X exists for all t ≥ t0. Such control u(·) and trajectory x(·) are call... more where u(t) ∈ U and x(t) ∈ X exists for all t ≥ t0. Such control u(·) and trajectory x(·) are called admissible. Functions f and g are differentiable w.r.t. their first argument, x, and together with those partial derivatives are defined and locally bounded, measurable in t for every (x, u) ∈ X × U , and continuous in (x, u) for almost every t ∈ [0,∞). In addition to the maximum principle we find a new form of necessary conditions for the two following concepts of optimality. An admissible control û(·) for which the corresponding trajectory x̂(·) exists on [t0,+∞) is overtaking optimal (OO) if for all admissible controls u(·)
Dynamic behavior of a weightless rod with a point mass sliding along the rod axis according to pe... more Dynamic behavior of a weightless rod with a point mass sliding along the rod axis according to periodic law is studied. This is the simplest model of child's swing. Melnikov's analysis is carried out to find bifurcations of homoclinic, subharmonic oscillatory, and subharmonic rotational orbits. For the analysis of superharmonic rotational orbits the averaging method is used and stability of obtained approximate solution is checked. The analytical results are compared with numerical simulation results.
Dynamic behavior of a weightless rod with a point mass sliding along the rod axis according to pe... more Dynamic behavior of a weightless rod with a point mass sliding along the rod axis according to periodic law is studied. This is the pendulum with periodically varying length which is also treated as a simple model of child's swing. Asymptotic expressions for boundaries of instability domains near resonance frequencies are derived. Domains for oscillation, rotation, and oscillation-rotation motions in parameter space are found analytically and compared with numerical study. Two types of transitions to chaos of the pendulum depending on problem parameters are investigated numerically.
To ensure the maneuvering capabilities of aircraft and high-speed sea vessels, designers should k... more To ensure the maneuvering capabilities of aircraft and high-speed sea vessels, designers should know the moments of inertia of their massive parts. But since the structure of some elements such as power units is very complicated, it is impossible to determine their moments of inertia analytically. Thus the problem of measuring the moments of inertia of massive large bodies arises.
A linear oscillator with limited excitation force (control function) is under consideration. The ... more A linear oscillator with limited excitation force (control function) is under consideration. The optimal control, which brings oscillatory system to a certain energy level from any initial conditions at the minimal time, is found. The synthesis of control is done. Multi-dimensional case is also studied. The problem has mechanical application to inertia moments measuring by oscillations of a rigid body in elastic support with several degrees of freedom.
Trudy ordena Lenina Matematičeskogo instituta im. V.A. Steklova, Nov 30, 2021
<jats:p>Оптимизируется сбор возобновляемого ресурса, распределенного на окружности. Динамик... more <jats:p>Оптимизируется сбор возобновляемого ресурса, распределенного на окружности. Динамика восстановления ресурса описывается уравнением типа Колмогорова-Петровского-Пискунова-Фишера в дивергентной форме, а сбор ресурса осуществляется движущейся циклически по окружности машиной, при этом в функционале качества учитываются положение этой машины, сложность обнаружения или сбора ресурса из этого положения, а также удаление ресурса от него. Доказано существование оптимального движения собирающей машины, доставляющего максимум средней временно́й выгоды в натуральном виде в долгосрочной перспективе при начальном распределении ресурса, не меньшем предельного при отсутствии сбора.</jats:p>
We analyze the effects of anticipated population aging within a general equilibrium R&D-based end... more We analyze the effects of anticipated population aging within a general equilibrium R&D-based endogenous growth model with overlapping generations. In doing so we model aging as a rise of longevity and a simultaneous drop in fertility. In contrast to an unanticipated rise of longevity, consumers increase their savings and reduce their consumption long before the rise of longevity actually happens. This implies that individuals save more in anticipation of aging, which puts downward pressure on the interest rate and raises economic growth through an increase in R&D incentives. Irrespective of the anticipation effect, the economic change at impact is not smooth but still features a kink in consumption.
where u(t) ∈ U and x(t) ∈ X exists for all t ≥ t0. Such control u(·) and trajectory x(·) are call... more where u(t) ∈ U and x(t) ∈ X exists for all t ≥ t0. Such control u(·) and trajectory x(·) are called admissible. Functions f and g are differentiable w.r.t. their first argument, x, and together with those partial derivatives are defined and locally bounded, measurable in t for every (x, u) ∈ X × U , and continuous in (x, u) for almost every t ∈ [0,∞). In addition to the maximum principle we find a new form of necessary conditions for the two following concepts of optimality. An admissible control û(·) for which the corresponding trajectory x̂(·) exists on [t0,+∞) is overtaking optimal (OO) if for all admissible controls u(·)
Dynamic behavior of a weightless rod with a point mass sliding along the rod axis according to pe... more Dynamic behavior of a weightless rod with a point mass sliding along the rod axis according to periodic law is studied. This is the simplest model of child's swing. Melnikov's analysis is carried out to find bifurcations of homoclinic, subharmonic oscillatory, and subharmonic rotational orbits. For the analysis of superharmonic rotational orbits the averaging method is used and stability of obtained approximate solution is checked. The analytical results are compared with numerical simulation results.
Dynamic behavior of a weightless rod with a point mass sliding along the rod axis according to pe... more Dynamic behavior of a weightless rod with a point mass sliding along the rod axis according to periodic law is studied. This is the pendulum with periodically varying length which is also treated as a simple model of child's swing. Asymptotic expressions for boundaries of instability domains near resonance frequencies are derived. Domains for oscillation, rotation, and oscillation-rotation motions in parameter space are found analytically and compared with numerical study. Two types of transitions to chaos of the pendulum depending on problem parameters are investigated numerically.
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Papers by Anton Belyakov