Vladimir Verbitskii - Academia.edu (original) (raw)
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Papers by Vladimir Verbitskii
The problem of the automobile course stability is considered. The changeable steering character b... more The problem of the automobile course stability is considered. The changeable steering character based on the analysis of non-linear velocipede model is analyzed. Generalized dependence determining “the steering curve” is obtained. Conditions caused the loss of stability with increasing speed while moving within the constant radius circle regarding the bifurcation set are analyzed. кубического двучлена.Розглянуто проблеми курсової стійкості руху автомобіля. В роботі аналізується зміна властивостей керованості на основі аналізу нелінійної велосипедної моделі, яка враховує нелінійність сил бокового відведення. Отримано узагальнену залежність, яка визначає «криву керованості». Проаналізовано умови втрати стійкості для випадку рухів зі зростаючою швидкістю по колу сталого радіуса на основі побудови біфуркаційної множини.Рассматриваются проблемы курсовой устойчивости движения автомобиля. В работе анализируется смена свойств управляемости на основе анализа нелинейной велосипедной модели, к...
The stability and shimmies of the front non-steerable pillar free to turn on two channels – the y... more The stability and shimmies of the front non-steerable pillar free to turn on two channels – the yaw and roll relative to the longitudinal axis of the body is analyzed. The analysis of the typical system parameters impact on the unstable oscillatory region and oscillation amplitude is carried out. The approximation percent influence of the slip force and heel moment on the oscillation character is considered.Аналізується стійкість та автоколивання передньої «некерованої» стійкі, що має свободу повороту за двома каналами – рисканню і креном відносно продольної осі корпусу. Запропоновано підхід наближеного аналізу автоколивань в нелінійній постановці, що дає можливість оцінити стійкість у «великому». Проведено аналіз впливу характерних параметрів системи на область коливальної нестійкості и амплітуди автоколивань (одержано аналітичний вираз, який зв‘язує амплітуду коливань з параметрами моделі: моментом інерції колеса відносно оси повороту, крутильною жорсткістю рульового керування, ко...
An alternative approach of the determining of conditions of safe stability loss of rectilinear mo... more An alternative approach of the determining of conditions of safe stability loss of rectilinear motion of a wheeled vehicle model with controlled wheel module in the sense of N.N. Bautin is considered. Skid forces are presented accurate within cubic expansion terms in the skid angles. Terms and conditions of safe stability loss depend on the ratio between the coefficients of resistance to the skid, the adhesion coefficients in the transverse direction of the axes and the parameter of torsional stiffness of the controlled wheel module.The presented approach to the analysis of real bifurcations related to the divergent loss of rectilinear motion mode stability has a clear geometric pattern: if in the vicinity of rectilinear motion at subcritical speed, there are additionally two unstable circular stationary states, then the stability limit is of dangerous nature in the sense of N. N. Bautin; if two circular stationary modes exist at supercritical speed, the limit of the stability loss ...
Mechanical Sciences, 2022
Abstract. This paper presents the bifurcation approach to analyze divergent loss of stability of ... more Abstract. This paper presents the bifurcation approach to analyze divergent loss of stability of the symmetric solution of a nonlinear dynamic model in Lyapunov's critical case of a single zero root. Under such a condition, material birth-annihilation bifurcations of multiple stationary states take place. Moreover, the equilibrium surface of stationary states in a small neighborhood of the symmetric solution is a generalized Whitney fold. In the simplest case of a fold peculiarity, the corresponding bifurcation manifold locally coincides with the discriminant manifold of a third-degree polynomial that determines the manifold of stationary states in a small neighborhood of the symmetric solution. An algorithm to construct the corresponding polynomial is introduced. Through the algorithm, the bifurcation manifold is determined, and the conditions for safe/unsafe loss of stability of the symmetric solution are derived analytically. The proposed approach to analyze divergent loss of...
The problem of the automobile course stability is considered. The change of the car steerability ... more The problem of the automobile course stability is considered. The change of the car steerability based on the analysis of non-linear bicycle model is analyzed. Generalized dependence determining “the steerability curve” is obtained. Conditions which caused the loss of stability with increasing speed while moving within the constant radius circle regarding the bifurcation set are analyzed. K e y w o r d s : car, stability, model, slip, bifurcation set.
TRANSPORT, ECOLOGY - SUSTAINABLE DEVELOPMENT EKO VARNA 2021, 2021
The article presents a bifurcation approach to analysis of stability of entire plenty of circular... more The article presents a bifurcation approach to analysis of stability of entire plenty of circular stationary modes of motion of a nonlinear model of a biaxial wheeled vehicle with oversteer. Its connection with classical (local) approach to stability analysis of stationary states of a dynamical system is discussed. The analytical conditions for divergent loss of stability of vehicle in curves of constant curvature and conditions for loss of stability in curve are turn.
MATEC Web of Conferences, 2018
This research investigates the stability of a two-wheeled vehicle model on the basis of numerical... more This research investigates the stability of a two-wheeled vehicle model on the basis of numerical determination of full range of eigenvalues of a linear approximation matrix in the vicinity of the rectilinear driving mode. The received result was checked by numerical integration of the initial equations system of the disturbed motion of the model. The discrepancy of two research techniques is explained by the specialty of the considered mathematical model in which two pairs of complex conjugate eigenvalues close to each other are realized, that explains the emergence of standard derivations at calculating their numerical determination. The model is asymptotically stable in the range much wider than an operational interval (up to 100 m/s). In order to provide more intensive dampening of initial disturbances, it is possible to introduce additional resilient and damping elements between the trucks and the body in the design of the wheeled vehicle that will counteract the yaw mode of tr...
The problem of the automobile course stability is considered. The changeable steering character b... more The problem of the automobile course stability is considered. The changeable steering character based on the analysis of non-linear velocipede model is analyzed. Generalized dependence determining “the steering curve” is obtained. Conditions caused the loss of stability with increasing speed while moving within the constant radius circle regarding the bifurcation set are analyzed. кубического двучлена.Розглянуто проблеми курсової стійкості руху автомобіля. В роботі аналізується зміна властивостей керованості на основі аналізу нелінійної велосипедної моделі, яка враховує нелінійність сил бокового відведення. Отримано узагальнену залежність, яка визначає «криву керованості». Проаналізовано умови втрати стійкості для випадку рухів зі зростаючою швидкістю по колу сталого радіуса на основі побудови біфуркаційної множини.Рассматриваются проблемы курсовой устойчивости движения автомобиля. В работе анализируется смена свойств управляемости на основе анализа нелинейной велосипедной модели, к...
The stability and shimmies of the front non-steerable pillar free to turn on two channels – the y... more The stability and shimmies of the front non-steerable pillar free to turn on two channels – the yaw and roll relative to the longitudinal axis of the body is analyzed. The analysis of the typical system parameters impact on the unstable oscillatory region and oscillation amplitude is carried out. The approximation percent influence of the slip force and heel moment on the oscillation character is considered.Аналізується стійкість та автоколивання передньої «некерованої» стійкі, що має свободу повороту за двома каналами – рисканню і креном відносно продольної осі корпусу. Запропоновано підхід наближеного аналізу автоколивань в нелінійній постановці, що дає можливість оцінити стійкість у «великому». Проведено аналіз впливу характерних параметрів системи на область коливальної нестійкості и амплітуди автоколивань (одержано аналітичний вираз, який зв‘язує амплітуду коливань з параметрами моделі: моментом інерції колеса відносно оси повороту, крутильною жорсткістю рульового керування, ко...
An alternative approach of the determining of conditions of safe stability loss of rectilinear mo... more An alternative approach of the determining of conditions of safe stability loss of rectilinear motion of a wheeled vehicle model with controlled wheel module in the sense of N.N. Bautin is considered. Skid forces are presented accurate within cubic expansion terms in the skid angles. Terms and conditions of safe stability loss depend on the ratio between the coefficients of resistance to the skid, the adhesion coefficients in the transverse direction of the axes and the parameter of torsional stiffness of the controlled wheel module.The presented approach to the analysis of real bifurcations related to the divergent loss of rectilinear motion mode stability has a clear geometric pattern: if in the vicinity of rectilinear motion at subcritical speed, there are additionally two unstable circular stationary states, then the stability limit is of dangerous nature in the sense of N. N. Bautin; if two circular stationary modes exist at supercritical speed, the limit of the stability loss ...
Mechanical Sciences, 2022
Abstract. This paper presents the bifurcation approach to analyze divergent loss of stability of ... more Abstract. This paper presents the bifurcation approach to analyze divergent loss of stability of the symmetric solution of a nonlinear dynamic model in Lyapunov's critical case of a single zero root. Under such a condition, material birth-annihilation bifurcations of multiple stationary states take place. Moreover, the equilibrium surface of stationary states in a small neighborhood of the symmetric solution is a generalized Whitney fold. In the simplest case of a fold peculiarity, the corresponding bifurcation manifold locally coincides with the discriminant manifold of a third-degree polynomial that determines the manifold of stationary states in a small neighborhood of the symmetric solution. An algorithm to construct the corresponding polynomial is introduced. Through the algorithm, the bifurcation manifold is determined, and the conditions for safe/unsafe loss of stability of the symmetric solution are derived analytically. The proposed approach to analyze divergent loss of...
The problem of the automobile course stability is considered. The change of the car steerability ... more The problem of the automobile course stability is considered. The change of the car steerability based on the analysis of non-linear bicycle model is analyzed. Generalized dependence determining “the steerability curve” is obtained. Conditions which caused the loss of stability with increasing speed while moving within the constant radius circle regarding the bifurcation set are analyzed. K e y w o r d s : car, stability, model, slip, bifurcation set.
TRANSPORT, ECOLOGY - SUSTAINABLE DEVELOPMENT EKO VARNA 2021, 2021
The article presents a bifurcation approach to analysis of stability of entire plenty of circular... more The article presents a bifurcation approach to analysis of stability of entire plenty of circular stationary modes of motion of a nonlinear model of a biaxial wheeled vehicle with oversteer. Its connection with classical (local) approach to stability analysis of stationary states of a dynamical system is discussed. The analytical conditions for divergent loss of stability of vehicle in curves of constant curvature and conditions for loss of stability in curve are turn.
MATEC Web of Conferences, 2018
This research investigates the stability of a two-wheeled vehicle model on the basis of numerical... more This research investigates the stability of a two-wheeled vehicle model on the basis of numerical determination of full range of eigenvalues of a linear approximation matrix in the vicinity of the rectilinear driving mode. The received result was checked by numerical integration of the initial equations system of the disturbed motion of the model. The discrepancy of two research techniques is explained by the specialty of the considered mathematical model in which two pairs of complex conjugate eigenvalues close to each other are realized, that explains the emergence of standard derivations at calculating their numerical determination. The model is asymptotically stable in the range much wider than an operational interval (up to 100 m/s). In order to provide more intensive dampening of initial disturbances, it is possible to introduce additional resilient and damping elements between the trucks and the body in the design of the wheeled vehicle that will counteract the yaw mode of tr...