scholarly journals Mathematical models of the gyrostabilizer in different modes of its operation

2021 ◽  
Author(s):  
Oleg Nesterenko ◽  
Lev Ryzhkov ◽  
Vladyslav Osokin
Keyword(s):  
Mathematical Model ◽  
Coordinate System ◽  
Dry Friction ◽  
Center Of Mass ◽  
Radius Vector ◽  
The Body ◽  
Line Of Sight ◽  
Rotation System ◽  
Angular Velocities ◽  
Kinetic Moment

The article considers the development of a mathematical model of the stabilization and rotation system in the modes of stabilization, targeting, auto-tracking of the target and electrical arrest. The output signals shall be signals proportional to the components of the angular velocities of the line of sight, the angles of pitch and dash of deviation around the axes of the gyrosystem and the angles of inconsistency of the line of sight relative to the optical axis of the homing head. The system of cardan suspension of the stabilization and rotation system is considered, where the actuators are located on the axes of rotation of the outer and inner frames of the cardan suspension. The homing head is mounted on the inner frame. The inner frame is a gyrostabilized platform. Depending on the mode of operation of the stabilization and rotation system: in the stabilization mode, the coordinate system that is stabilized is assumed to be stationary in inertial space; in the auto-tracking mode of the target, the coordinate system that is stabilized by Oxyz is returned according to the change of direction to the target; in the mode of electrical locking, the axes of the coordinate system which is stabilized by Oxyz coincide with the axes of Oxoyozo connected to the body of the main product. To obtain differential equations, the projections of the total vector of the kinetic moment of the inner and outer frames on the axis of the outer frame are taken and written according to the theorem on the change of the kinetic moment of the considered system relative to the axes of suspensions. The total moments of external forces applied to the outer and inner frames around their axes of rotation, which have the following components: moments of actuators, moments of viscous and dry friction, imbalance and other unaccounted for factors around the axes of the outer and inner frames . The moments of the forces of viscous and dry friction are presented in the classical form, taking into account the signs when changing the direction of movement. The mass of the inner frame with all devices mounted on it, and the mass of the entire movable system (outer and inner frames), as well as the radius vector characterizing the displacement of the center of mass, give a static imbalance of the movable system relative to the suspension axis of the i-th frame are components imbalance. The scientific novelty of the work is to obtain a mathematical model for a particular product, as well as the practical feasibility of their application. The result is a differential equation that fully describes this system of stabilization and rotation, takes into account the parameters of actuators, turbulent moments, as well as random effects and can be used depending on the tasks.

A Mathematical "Screw-Nut" Connection Model for the Universal Software to Analyse Dynamical Systems

2017 ◽  
pp. 1-12
Author(s):  
V. A. Martynyuk ◽  
V. A. Trudonoshin ◽  
V. G. Fedoruk
Keyword(s):  
Mathematical Model ◽  
Coordinate System ◽  
Dry Friction ◽  
Local Coordinate System ◽  
Direction Cosine ◽  
The Body ◽  
Global Coordinate System ◽  
Elastic Model ◽  
Screw Axis ◽  
The Mathematical Model

The article deals with a mathematical model of the "screw-nut" connection adapted for using in universal software systems to analyse dynamic characteristics. This article is sequel to a number of earlier authors-written articles devoted to object simulation of 3D mechanics. Such a model available in the library of mathematical models of the modelling system will significantly extend the list of simulated mechanisms. The mathematical model of "screw-nut" connection suggests such a connection between absolutely rigid bodies. The "screw-nut" connection parameters are the following:thread pitch by the radian of the angle of pitch;coordinates of the point on the axis of the screw in the local coordinate system of the body 1;direction cosines of the screw axis in the local coordinate system of the body 1.Note that the connection parameters have constant values. Two drawbacks of this model should be noted.1. Some expressions of the mathematical model involve dividing by direction cosine  of the screw axis thereby eliminating "division by zero" when the axis of the screw is perpendicular to the x-axis of the global coordinate system. The software-based way allows eliminating this shortcoming.2. The model does not include coordinates of mass centres of bodies tied by connection. This can lead to a significant "mismatch" in the position of the bodies in modelling of multi- periodic transient processes. However, adding an elastic model to the mathematical model can eliminate this drawback.The article demonstrates the "screw-nut" connection model to simulate a jack using the PA8 system and comparing its results with those obtained with help of the NX10 complex. Gives, in addition, the results of influence in terms of dry friction in the "screw-nut" connection. Taking into consideration the dry friction allows us to reflect the effect of "self-stopping" in the jack.

On the motion of bodies based on changes in the kinetic moment

2019 ◽  
Vol 20 (4) ◽  
pp. 267-275
Author(s):  
Yury N. Razoumny ◽  
Sergei A. Kupreev
Keyword(s):  
Center Of Mass ◽  
Stellar Dynamics ◽  
Elementary Particles ◽  
The Body ◽  
Accelerated Motion ◽  
Indirect Confirmation ◽  
Physical Principles ◽  
Two Bodies ◽  
Central Gravitational Field ◽  
Kinetic Moment

The controlled motion of a body in a central gravitational field without mass flow is considered. The possibility of moving the body in the radial direction from the center of attraction due to changes in the kinetic moment relative to the center of mass of the body is shown. A scheme for moving the body using a system of flywheels located in the same plane in near-circular orbits with different heights is proposed. The use of the spin of elementary particles is considered as flywheels. It is proved that using the spin of elementary particles with a Compton wavelength exceeding the distance to the attracting center is energetically more profitable than using the momentum of these particles to move the body. The calculation of motion using hypothetical particles (gravitons) is presented. A hypothesis has been put forward about the radiation of bodies during accelerated motion, which finds indirect confirmation in stellar dynamics and in an experiment with the fall of two bodies in a vacuum. The results can be used in experiments to search for elementary particles with low energy, explain cosmic phenomena and to develop transport objects on new physical principles.

scholarly journals MATHEMATICAL MODEL FOR SOLVING THE NAVIGATION PROBLEM AND ANGULAR ORIENTATION SPACECRAFT

2019 ◽  
Vol 27 (4) ◽  
pp. 101-108
Author(s):  
Ilya Andreevich Sidorov ◽  
Alexander Alekseevich Manoilenko
Keyword(s):  
Mathematical Model ◽  
Moving Average ◽  
Center Of Mass ◽  
Exponential Smoothing ◽  
Infinite Impulse Response ◽  
Navigation Systems ◽  
Angular Orientation ◽  
Magnetometer Data ◽  
Angular Velocities ◽  
The Mathematical Model

Currently, there is an increased interest in the creation of strapdown inertial navigation systems (SINS), which make up the information core of modern airborne systems for the orientation and navigation of spacecraft (SC). An urgent problem arises, which is associated with the development of high-precision algorithms for estimating and filtering data from the sensors of the SC  motion parameters, the mathematical model of the SINS, calculating its errors and analyzing the effect of errors on the characteristics of the navigation system and orientation of the SC. A mathematical model is proposed for solving the problem of navigation and angular orientation of a small SC equipped with electromagnetic control elements, taking into account the filtering of “noisy” magnetometer data. The requirements are set for the accuracy of the angular orientation and stabilization of the SC in the mode of maintaining the triaxial orientation of the SC in the orbital coordinate system (OCS) and for the duration of the damping mode of the angular velocities obtained by the SC during separation from the launch vehicle (LV), and the mode of the initial construction of the triaxial orientation of the SC in OCS. The mathematical model includes: a model of the motion of the center of mass of the SC in the osculating elements of the orbit with specified parameters, a model of the angular motion of the SC around the center of mass, a model of the Earth’s magnetic field (EMF) and a model of filtering magnetometer data. As an arithm for filtering data from a magnetometer on the components of the magnetic induction vector of the EMF, a one-parameter algorithm of exponential smoothing (exponential moving average) is used, which belongs to the class of first-order filters with an infinite impulse response. The results of numerical simulation of  the dynamic processes of navigation and the angular orientation of the SC after separation from the LV taking into account the filtering of magnetometer data by the method of exponential smoothing using mathematical models are presented, and the accuracy of the angular orientation and stabilization of the SC is estimated.

A Biomechanical Assessment of the Sliding Motion of Curling Delivery in Elite and Subelite Curlers

2012 ◽  
Vol 28 (6) ◽  
pp. 694-700 ◽  
Author(s):  
Kyoung-Seok Yoo ◽  
Hyun-Kyung Kim ◽  
Jin-Hoon Park
Keyword(s):  
Balance Control ◽  
Center Of Mass ◽  
Three Dimensional ◽  
The Body ◽  
Movement Speed ◽  
Biomechanical Assessment ◽  
Sliding Motion ◽  
Angular Velocities ◽  
Posterior Direction ◽  
The Moment

The present study examined the technical characteristics of sliding performance from push-off until stone release in curling delivery. Five elite performance level curlers (> 7 years experience) and five subelite level curlers (< 3 years experience) were analyzed during the action of delivery of a curling stone. The joint angles, angular velocities, and moments of the body center of mass (COM) were determined based on three-dimensional kinematic data. The plantar pressure data were measured using a validated in-shoe system. The results indicated that the gliding time and horizontal velocity of the mass center of the body during the sliding phase were not significantly different between the elite and subelite groups. However, there were significant differences in the gliding distance and the rate of changes in velocity profiles of body COM between the two groups. The moment of the body COM from its relative position to the ankle of the support limb in the anterior/posterior direction was positive in elite curlers and negative in subelite curlers. In addition, larger ankle dorsiflexion and greater contact area of the sliding foot were observed in elite curlers. These data suggest a superior ability of elite curlers to maintain a regulated movement speed and balance control during the performance of a curling stone delivery.

TO THE STABILITY OF TANK VEHICLES IN THE BRAKE MODE

2019 ◽  
pp. 27-32
Author(s):  
Denys Popelysh ◽  
Yurii Seluk ◽  
Sergyi Tomchuk
Keyword(s):  
Mathematical Model ◽  
Control Systems ◽  
Distribution Systems ◽  
Traffic Accidents ◽  
Road Traffic ◽  
Center Of Mass ◽  
Dynamic Processes ◽  
Course Stability ◽  
The Stability ◽  
Tank Vehicles

This article discusses the question of the possibility of improving the roll stability of partially filled tank vehicles while braking. We consider the dangers associated with partially filled tank vehicles. We give examples of the severe consequences of road traffic accidents that have occurred with tank vehicles carrying dangerous goods. We conducted an analysis of the dynamic processes of fluid flow in the tank and their influence on the basic parameters of the stability of vehicle. When transporting a partially filled tank due to the comparability of the mass of the empty tank with the mass of the fluid being transported, the dynamic qualities of the vehicle change so that they differ significantly from the dynamic characteristics of other vehicles. Due to large displacements of the center of mass of cargo in the tank there are additional loads that act vehicle and significantly reduce the course stability and the drivability. We consider the dynamics of liquid sloshing in moving containers, and give examples of building a mechanical model of an oscillating fluid in a tank and a mathematical model of a vehicle with a tank. We also considered the method of improving the vehicle’s stability, which is based on the prediction of the moment of action and the nature of the dynamic processes of liquid cargo and the implementation of preventive actions by executive mechanisms. Modern automated control systems (anti-lock brake system, anti-slip control systems, stabilization systems, braking forces distribution systems, floor level systems, etc.) use a certain list of elements for collecting necessary parameters and actuators for their work. This gives the ability to influence the course stability properties without interfering with the design of the vehicle only by making changes to the software of these systems. Keywords: tank vehicle, roll stability, mathematical model, vehicle control systems.

scholarly journals Effect of foot–floor friction on the external moment about the body center of mass during shuffling gait: a pilot study

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Takeshi Yamaguchi ◽  
Kei Shibata ◽  
Hiromi Wada ◽  
Hiroshi Kakehi ◽  
Kazuo Hokkirigawa
Keyword(s):  
Friction Surface ◽  
Center Of Mass ◽  
Young Male ◽  
The Body ◽  
Low Friction ◽  
Surface Conditions ◽  
Normal Gait ◽  
External Moment ◽  
Body Center ◽  
Floor Condition

AbstractHerein, we investigated the effect of friction between foot sole and floor on the external forward moment about the body center of mass (COM) in normal and shuffling gaits. Five young male adults walked with normal and shuffling gaits, under low- and high-friction surface conditions. The maximum external forward moment about the COM (MEFM-COM) in a normal gait appeared approximately at initial foot contact and was unaffected by floor condition. However, MEFM-COM in a shuffling gait under high-friction conditions exceeded that under low-friction conditions (p < 0.001). Therein, MEFM-COM increased with an increasing utilized coefficient of friction at initial foot contact; this effect was weaker during a normal gait. These findings indicate that increased friction between foot sole and floor might increase tripping risk during a shuffling gait, even in the absence of discrete physical obstacles.

scholarly journals Zur exakten Behandlung von kollektiven Rotationen Teil A: Theorie / On the Exact Treatment of Collective Rotations Part A: Theory

1973 ◽  
Vol 28 (2) ◽  
pp. 206-215
Author(s):  
Hanns Ruder
Keyword(s):  
Coordinate System ◽  
Perturbation Expansion ◽  
Rotational Energy ◽  
The Body ◽  
System A ◽  
N Body Problem ◽  
Definition Of ◽  
Fixed System ◽  
Body Fixed Coordinate System ◽  
Groundstate Energy

Basic in the treatment of collective rotations is the definition of a body-fixed coordinate system. A kinematical method is derived to obtain the Hamiltonian of a n-body problem for a given definition of the body-fixed system. From this exact Hamiltonian, a consequent perturbation expansion in terms of the total angular momentum leads to two exact expressions: one for the collective rotational energy which has to be added to the groundstate energy in this order of perturbation and a second one for the effective inertia tensor in the groundstate. The discussion of these results leads to two criteria how to define the best body-fixed coordinate system, namely a differential equation and a variational principle. The equivalence of both is shown.

Impact of Electric Vehicle Lateral Dynamics on the Battery Pack

2014 ◽  
Vol 590 ◽  
pp. 451-457
Author(s):  
Sen Nan Song ◽  
Fa Chao Jiang ◽  
Hong Shi
Keyword(s):  
Mathematical Model ◽  
Angular Acceleration ◽  
Simulation Software ◽  
The Body ◽  
Battery Pack ◽  
Vehicle Body ◽  
Rolling Motion ◽  
Rolling Angle ◽  
On The Road ◽  
The Mathematical Model

The present work is concerned with the rolling motion of the battery pack when EV travelling on the road. First McPherson suspension system was regarded as the research object with detailed analysis of its structural features and motion characteristics. Establish the mathematical model which could apply to calculating the rolling motion of the vehicle body. Through MATLAB/Simulink simulation software, we could calculate the rolling angle on passive suspension. On this basis, assume that the battery pack mounted on the vehicle body and make it passive connection and PID connection. When the body rolls, the battery pack will produce a certain angle then. Next establish the mathematical model to summarize the relationship between the two variables. Then we set the parameters and calculate the roll angle of battery pack in both cases for comparison. Simulation results show that road irregularities will make battery rotate an angle and PID controller can effectively reduce the angle, especially angular acceleration. This paper put forward a new idea that battery is connected with body by active control on EV, and proves the superiority in reducing the rolling angle.

The physical basis of mollusk shell chiral coiling

2021 ◽  
Vol 118 (48) ◽  
pp. e2109210118
Author(s):  
Régis Chirat ◽  
Alain Goriely ◽  
Derek E. Moulton
Keyword(s):  
Mathematical Model ◽  
The Body ◽  
Symmetric Body ◽  
Model Organisms ◽  
Physical Interaction ◽  
Mechanical Forces ◽  
Hard Shell ◽  
Left Right Asymmetry ◽  
Development And Evolution ◽  
Mollusk Shell

Snails are model organisms for studying the genetic, molecular, and developmental bases of left–right asymmetry in Bilateria. However, the development of their typical helicospiral shell, present for the last 540 million years in environments as different as the abyss or our gardens, remains poorly understood. Conversely, ammonites typically have a bilaterally symmetric, planispiraly coiled shell, with only 1% of 3,000 genera displaying either a helicospiral or a meandering asymmetric shell. A comparative analysis suggests that the development of chiral shells in these mollusks is different and that, unlike snails, ammonites with asymmetric shells probably had a bilaterally symmetric body diagnostic of cephalopods. We propose a mathematical model for the growth of shells, taking into account the physical interaction during development between the soft mollusk body and its hard shell. Our model shows that a growth mismatch between the secreted shell tube and a bilaterally symmetric body in ammonites can generate mechanical forces that are balanced by a twist of the body, breaking shell symmetry. In gastropods, where a twist is intrinsic to the body, the same model predicts that helicospiral shells are the most likely shell forms. Our model explains a large diversity of forms and shows that, although molluscan shells are incrementally secreted at their opening, the path followed by the shell edge and the resulting form are partly governed by the mechanics of the body inside the shell, a perspective that explains many aspects of their development and evolution.

Numerical modelling of swirling momentumless turbulent wake dynamics

2018 ◽  
pp. 37-48
Author(s):  
Андрей Геннадьевич Деменков ◽  
Геннадий Георгиевич Черных
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Equations Of Motion ◽  
Turbulent Wake ◽  
The Body ◽  
Jet Flows ◽  
Reynolds Stresses ◽  
Bodies Of Revolution ◽  
Averaged Equations

С применением математической модели, включающей осредненные уравнения движения и дифференциальные уравнения переноса нормальных рейнольдсовых напряжений и скорости диссипации, выполнено численное моделирование эволюции безымпульсного закрученного турбулентного следа с ненулевым моментом количества движения за телом вращения. Получено, что начиная с расстояний порядка 1000 диаметров от тела течение становится автомодельным. На основе анализа результатов численных экспериментов построены упрощенные математические модели дальнего следа. Swirling turbulent jet flows are of interest in connection with the design and development of various energy and chemical-technological devices as well as both study of flow around bodies and solving problems of environmental hydrodynamics, etc. An interesting example of such a flow is a swirling turbulent wake behind bodies of revolution. Analysis of the known works on the numerical simulation of swirling turbulent wakes behind bodies of revolution indicates lack of knowledge on the dynamics of the momentumless swirling turbulent wake. A special case of the motion of a body with a propulsor whose thrust compensates the swirl is studied, but there is a nonzero integral swirl in the flow. In previous works with the participation of the authors, a numerical simulation of the initial stage of the evolution of a swirling momentumless turbulent wake based on a hierarchy of second-order mathematical models was performed. It is shown that a satisfactory agreement of the results of calculations with the available experimental data is possible only with the use of a mathematical model that includes the averaged equations of motion and differential equations for the transfer of normal Reynolds stresses along the rate of dissipation. In the present work, based on the above mentioned mathematical model, a numerical simulation of the evolution of a far momentumless swirling turbulent wake with a nonzero angular momentum behind the body of revolution is performed. It is shown that starting from distances of the order of 1000 diameters from the body the flow becomes self-similar. Based on the analysis of the results of numerical experiments, simplified mathematical models of the far wake are constructed. The authors dedicate this work to the blessed memory of Vladimir Alekseevich Kostomakha.

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