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1
Content available remote Numerical study of coupled oscillator system usingthe classical Euler-Lagrange equations
Shanak H., Khalilia H., Jarrar R., Asad J.
Mechanics and Mechanical Engineering
|
2021
|
Vol. 25, nr 1
1--5
EN
Problems involving vibrations (mechanical orelectrical) can be reduced to problems of coupled oscil-lators. For this, we consider the motion of coupled oscilla-tors system using Lagrangian method. The Lagrangian ofthe system was initially constructed, and then the Euler-Lagrange equations (i.e., equations of motion of the system)have been obtained. The obtained equations of motion are ahomogenous second-order equation. These equations weresolved numerically using the ode45 code, which is basedon Runge-Kutta method.
2
Content available Experimental studies and modeling of four-wheeled mobile robot motion taking into account wheel slippage
Jaskot Anna, Posiadała Bogdan
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2021
|
Vol. 69, nr 6
art. no. e139205
EN
In the article the results of simulation and experimental studies of the movement of a four-wheeled mobile platform, taking into account wheel slip have been presented. The simulation results have been based on the dynamics of the four-wheel mobile platform. The dynamic model of the system motion takes into account the relationship between the active and passive forces accompanying the platform motion, especially during wheel slip. The formulated initial problem describing the motion of the system has been solved by the Runge-Kutta method of the fourth order. The proposed computational model including the platform dynamics model has been verified in experimental studies using the LEO Rover robot. The motion parameters obtained on the basis of the adopted computational model in the form of trajectories, velocities and accelerations have been compared with the results of experimental tests, and the results of this comparison have been included in the paper. The proposed computational model can be useful in various situations, e.g., real-time control, where models with a high degree of complexity are useless due to the computation time. The simulation results obtained on the basis of the proposed model are sufficiently compatible with the results of experimental tests of motion parameters obtained for the selected type of mobile robot.
3
Content available Explicit form of the “modified point mass trajectory model” for the use in Fire Control Systems
Baranowski L., Majewski P., Szymonik J.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2020
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Vol. 68, nr 5
1167--1175
EN
The main objective of this article is to obtain equations of motion of the spin–stabilized projectile in the presence of non–constant wind. Introducing models allowing utilization of inhomogeneous wind is dictated by new possibilities created by the use of e.g. lidars in the Fire Control Systems (FCS). Constant feed of wind data can replace meteorological messages, increasing the FCS effectiveness. Article contains results of projectile flight simulations which indicate the positive effect that the derived explicit form of the model has when considering software development for modern Fire Control Systems.
4
Content available Mathematical model of levitating cart of magnetic UAV catapult
Sibilska-Mroziewicz A., Ładyżyńska-Kozdraś E.
Journal of Theoretical and Applied Mechanics
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2018
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Vol. 56 nr 3
793--802
EN
The article presents the steps of modeling of the dynamics of a levitating cart of an unmanned aerial vehicle (UAV) magnetic catapult. The presented in the article innovative catapult is based on the Meissner effect occurring between high-temperature superconductors (HTS) and a magnetic field source. The catapult suspension system consists of two elements: fixed to the ground base with magnetic rails and a moving cart. Generating magnetic field rails are made of neodymium magnets. Levitation of the launcher cart is caused by sixteen superconductors YBCO, placed in the cart frame supports. Described in the article model contains the system of Cartesian reference frames, kinematic constrains, equations of motion and description of forces acting on the cart as well as exemplary numerical simulation results.
5
Content available Comparison of explicit and implicit forms of the modified point mass trajectory model
Baranowski L., Gadomski B., Szymonik J., Majewski P.
Journal of Theoretical and Applied Mechanics
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2016
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Vol. 54 nr 4
1183--1195
EN
The article compares the results of trajectory computation for a 35 mm projectile using two forms (explicit and implicit) of the modified point-mass trajectory model. All necessary ammunition parameters (aerodynamic coefficients, dimensions, mass etc.) and initial conditions for differential equations are provided. The results of numerical integration (using non-stiff fourth-order Runge-Kutta solver) are presented in form of projectile trajectories projections onto vertical and horizontal planes. Data tables comparing both models in terms of projectile position and velocity in chosen time steps are also attached.
6
Content available Explicit “ballistic M-model”: a refinement of the implicit “modified point mass trajectory model”
Baranowski L., Gadomski B., Majewski P., Szymonik J.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2016
|
Vol. 64, nr 1
81--89
EN
Various models of a projectile in a resisting medium are used. Some are very simple, like the “point mass trajectory model”, others, like the “rigid body trajectory model”, are complex and hard to use, especially in Fire Control Systems due to the fact of numeric complexity and an excess of less important corrections. There exist intermediate ones - e.g. the “modified point mass trajectory model”, which unfortunately is given by an implicitly defined differential equation as Sec. 1 discusses. The main objective of this paper is to present a way to reformulate the model obtaining an easy to solve explicit system having a reasonable complexity yet not being parameter-overloaded. The final form of the M-model, after being carefully derived in Sec. 2, is presented in Subsec. 2.5.
7
Content available Modelowanie i symulacja numeryczna samonaprowadzania pocisku rakietowego na cel naziemny z wykorzystaniem sterowanego giroskopu
Ładyżyńska-Kozdraś E., Koruba Z.
Problemy Mechatroniki : uzbrojenie, lotnictwo, inżynieria bezpieczeństwa
|
2014
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Vol. 5, Nr 3 (17)
35-50
PL
W pracy zaprezentowano modelowanie dynamiki pocisku rakietowego, stabilizowanego przy użyciu giroskopu, samonaprowadzającego się na manewrujący cel naziemny. Model matematyczny opracowany został przy zastosowaniu równań Boltzmanna–Hamela dla układów mechanicznych o więzach nieholonomicznych. Pokazano, jak stosując ogólny model matematyczny sterowanego obiektu latającego, wprowadzając prawa sterowania jako więzy nieholonomiczne oraz stabilizację giroskopową, można sterować automatycznie badanym obiektem. Wprowadzone prawa sterowania stanowią związki kinematyczne uchybów, to znaczy różnic między parametrami zadanymi i realizowanymi lotu pocisku rakietowego. Otrzymane prawa sterowania potraktowano jako więzy nieholonomiczne ograniczające ruch pocisku tak, aby spełniał on żądany manewr sterowany. Związki kinematyczne i kryteria naprowadzania stanowią koordynację lotu sterowanej automatycznie rakiety, której ruch został powiązany z linią obserwacji manewrującego przestrzennie celu, wyznaczoną przez oś sterowanego giroskopu. Poprawność opracowanego modelu matematycznego potwierdziła symulacja numeryczna przeprowadzona dla pocisku klasy „Maverick” wyposażonego w giroskop będący elementem wykonawczym skanowania powierzchni ziemi i śledzenia wykrytego na niej celu. Analizie poddana została zarówno dynamika giroskopu, jak i pocisku podczas procesu śledzenia wykrytego celu. Wyniki przedstawione zostały w postaci graficznej.
EN
The paper presents the modelling of the dynamics of a self-guided missile steered using a gyroscope. In such kinds of missiles, attacking the targets detected by them, the main element is a self-guiding head, which is operated by a steered gyroscope. A mathematical model was precluded using the Boltzmann–Hamel equations for mechanical systems with non-holonomic constraints. A relatively simple method for automatic control has been presented based on introducing the control laws and gyroscope into a general model of a flying object. These control laws have the form of kinematics relations between the real and preset flight parameters, respectively. The resulting control laws are considered as non-holonomic constraints of the missile motion ensuring that it executes the specified controlled manoeuvre. Kinematical relations combined with homing criteria represent the coupling between the missile flight and 3D motion of a manoeuvring target. Correctness of the developed mathematical model was confirmed by digital simulation conducted for a Maverick missile equipped with a gyroscope being an executive element of the system scanning the earth’s surface and following the detected target. Both the dynamics of the gyroscope and the missile during the process of scanning and following the detected target were the subject to digital analysis. The results were presented in graphic form.
8
Content available Vertical vibrations of composite bridge/track structure/high-speed train systems. Part 2: Physical and mathematical modelling
Podworna M., Klasztorny M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2014
|
Vol. 62, nr 1
181--196
EN
A theory of one-dimensional physical and mathematical modelling of the composite (steel-concrete) bridge/track structure/highspeed train system is developed including viscoelastic suspensions of rail-vehicles with two two-axle bogies each, non-linear Hertz contact stiffness and one-sided contact between wheel sets and rails, the viscoelastic and inertia features of the bridge, the viscoelastic track structure on and beyond the bridge, approach slabs, and random vertical track irregularities. Compared to the state-of-the-art, the physical model developed in the study accurately reproduces dynamic processes in the considered system. Division of the system into the natural subsystems, a method of formulation of the equations of motion partly in implicit form and the finite element method are applied. Vibrations in the vertical plane of symmetry are described by more than nine matrix equations of motion with constant coefficients. Couplings and non-linearity are hidden in the generalized load vectors. The equations of motion are integrated using the implicit Newmark average acceleration method with linear extrapolation of the interactions between the subsystems.
9
Content available Feasibility analysis of the modified point mass trajectory model for the need of ground artillery fire control systems
Baranowski L.
Journal of Theoretical and Applied Mechanics
|
2013
|
Vol. 51 nr 3
511--522
EN
The work shows computational results of the effect of a simplified mathematical model of the flight dynamics of a spin-stabilized projectile on the accuracy and speed of calculation parameters for the projectile trajectory (in the entire range of operating quadrant elevation of the barrel and possible perturbations of the conditions firing) to determine an appropriate mathematical model for the automated fire control systems of ground artillery.
10
Content available remote Równania ruchu i bilans mocy układu elektromechanicznego na przykładzie silnika eluktancyjnego
Wciślik M., Suchenia K., Zagniński P.
Przegląd Elektrotechniczny
|
2012
|
R. 88, nr 12b
325-328
PL
W literaturze występują różne postacie równań opisujących część elektryczną. Dla sprawdzenia postaci równań ruchu wykonano jednofazowy silnik reluktancyjny. Przeprowadzono identyfikację parametrów tego silnika w funkcji kąta obrotu wirnika zasilając uzwojenia napięciem przemiennym 50Hz. Na osi wirnika zamocowano prostopadle metalowy pręt, który umożliwiał oscylacje układu mechanicznego. Na podstawie oscylacji tego wahadła określono parametry układu mechanicznego. Przeprowadzono badania charakterystyki statycznej oraz parametrów dynamiki układu. Porównano parametry równania ruchu otrzymanego z eksperymentu z równaniami ruchu Lagrange’a drugiego rzędu. Przedstawiono metodykę otrzymywania tego równania wraz z dyskusją holonomiczności układów elektromechanicznych.
EN
In the literature there are different forms of equations describing the electrical component. The authors performed single-phase reluctance motor to test the motion equations. The identification of the motor parameters as a function of the rotation angle the rotor. Was carried out for 50 Hz alternating supply alternating voltage. Mechanical system was assumed as a system which can oscillate as the element of physical pendulum containing the motor rotor and perpendicularly to axis mounted metal bar. The mechanical system parameters were measured during the pendulum moving. The work deals with the characteristics and parameters of system dynamics. The article compares parameters of the equations motion obtained from experiment with Lagrange’a equations of second order. It presents the methodology of obtaining this equation, along with a discussion of holonomic electromechanical systems.
11
Content available remote External Dynamics of Hand Operated Hydraulic Hammer
Auguściński A., Talaśka K., Wilczyński D.
Machine Dynamics Problems
|
2008
|
Vol. 32, No. 1
7-13
EN
Structure of hand operated hydraulic hammer was discussed in the paper. There was proposed a dynamic model of system, which describes the motion of ram and housing of hammer. There were conducted simulations based on composed equations of motion. Results of experimental examinations concerning behaviour of housing during working of tool were presented. There was performed the comparison of simulation and experimental results on real object.
12
Content available Model trajektorii lotu pocisku wirującego o sześciu stopniach swobody zgodny ze Stanagiem 4355
Baranowski L.
Biuletyn Wojskowej Akademii Technicznej
|
2008
|
Vol. 57, nr 3
155-172
PL
W pracy przedstawiono sposób konstruowania modelu matematycznego dynamiki lotu pocisków stabilizowanych obrotowo, w którym pocisk traktowany jest jako osiowosymetryczna bryła sztywna o sześciu stopniach swobody. Zastosowano nazewnictwo i oznaczenia zgodne ze Stanagiem 4355 ed.4 [7]. Wektorowa postać równań ruchu pocisku jest zaktualizowaną wersją równań opublikowanych w pracy [3]. Skalarne równania zarówno ruchu postępowego, jak i obrotowego wyprowadzono w układzie związanym z Ziemią, wykorzystując zamiast kątów Eulera, cosinusy kierunkowe osi symetrii pocisku.
EN
In the paper, the equations of motion of a spin-stabilized, dynamically stable, conventional artillery projectile, possessing at least trigonal symmetry were introduced. The vector six degrees of freedom (6-DOF) differential equations of motion are an updated edition of those published at the BRL in report [1] and are consistent with Stanag 4355 [2]. This model is formulated to solve the projectile pitching and yawing motion in terms of direction cosines of the projectile's axis of symmetry, rather than the Euler-angle method.
13
Content available remote Recursive Formulation For The Dynamic Simulation of Multibody Systems
Attia H. A.
Mechanics and Mechanical Engineering
|
2007
|
Vol. 11, nr 1
5-19
EN
In this paper, recursive dynamic formulation for the dynamic simulation of multibody systems are presented. The method uses the concepts of linear and angular momentums to generate the rigid body equations of motion in terms of the Cartesian coordinates of a dynamically equivalent constrained system of particles, without introducing any rotational coordinates and the corresponding rotational transformation matrix. For the open-chain system, the equations of motion are generated recursively along the serial chains. Closed-chain system is transformed to open-chain by cutting suitable kinematic joints and introducing cut-joint constraints. An example is chosen to demonstrate the generality and simplicity of the developed formulation.
14
Content available remote Investigation of Dynamics and Control of the Single-Wheel Vehicle
Sanh D., Dihn V. P., Do D. K., Tran D.
Machine Dynamics Problems
|
2007
|
Vol. 31, No. 4
46-56
EN
In the presented paper, the problem of controlling a one-wheel vehicle is investigated. In connection with this problem, a hybrid method of both passive and active methods is applied. By means of the motion of an elliptic pendulum (passive controls) and the couple of forces of a servomotor (active controls) the unbalanced motion of the vehicle is controlled. The stated problem is solved by the theory of optimization of Hamilton and the method of constructing program constraints. A numerical algorithm is introduced, which is generalized for optimal problems of mechanical systems in the sense of stabilization.
15
Content available Wykorzystanie programu Mathematica do modelowania i analizy równań ruchu
Lubnauer W. A.
Biuletyn Wojskowej Akademii Technicznej
|
2007
|
Vol. 56, nr sp.1
71-85
PL
W pracy przedstawiono możliwości wykorzystania pakietu oprogramowania Mathematica firmy Wolfram Research. Na przykładzie modelu wahadła pokazano, jak przy pomocy Mathematici rozwiązywać różniczkowe równania ruchu i jakie są możliwości wizualizacji otrzymywanych wyników.
EN
The article presents ways of using Wolfram Research Company's software package Mathematica. The example of a pendulum model shows how Mathematica programe helps with solving differential equations of motion and the possibilities of visual presentation of the received results.
16
Asymmetric continuum mechanics: deviations from elasticity and symmetry
Teisseyre R.
Acta Geophysica Polonica
|
2005
|
Vol. 53, nr 2
115-126
EN
The Kröner approach to continua with a distribution of self-field sources is applied to a wide class of deviations from the classical ideal elasticity; the same approach is applied to the theory of continua with asymmetric fields. The corresponding equations of motion are derived. Such an approach replaces other methods based on the constitutive relations specific for each type of the medium; here, the reference constitutive relation remains the same, but deviations from the classical ideal elasticity are attributed to different sources and defects introduced into continuum theory. Both methods lead to the expressions for the related currents. The nuclei responsible for the deviations from classical elasticity can be related to the defect distribution (dislocation and disclination densities), thermal excitation, some features of internal structure and different types of nuclei (e.g. electric nuclei, rotation nuclei); other deviations lead to an elastoplastic behavior. Our considerations extend also on deviations from the stress symmetry and related incompatibilities; we consider the resulting equations of motion.
17
Spin and twist motions in a homogeneous elastic continuum and cross-band geometry of fracturing
Teisseyre R.
Acta Geophysica Polonica
|
2004
|
Vol. 52, nr 2
173-183
EN
A uniform continuum with rotation motions of spin and twist type is presented; in this approach we supplement the ideal elasticity constitutive law, the strain-stress relation, by the rotation-asymmetric stress relation. In such a way, we can evade an influence of the Hook law, which, when used as the unique law in the ideal elasticity, rules out an existence of rotation waves. Thus, in the ideal elastic continuum the rotation vibrations can propagate and are not attenuated. The asymmetric elastic rotation fields and their relation to asymmetric elastic stresses are proposed and discussed, under the condition that the total fields with the elastic and self parts remain symmetric or antisymmetric as required by the compatibility conditions. The tensor of incompatibility splits into the symmetric or antisymmetric parts. The conservation and balance laws for spin and twist fields and the stress -related equations of motion for symmetric and antisymmetric parts of stresses are given. The relations obtained for elastic fields, expressed by difference of the total and self-fields, can be split into the self-parts prevailing on the fracture plane and the total parts describing seismic radiation field in a surrounding space. The role of rotation processes in premonitory and rebound time domains is considered in estimating the most effective fracture patterns.
18
Generalized continuum with defects and asymmetric stresses
Boratyński W., Teisseyre R.
Acta Geophysica Polonica
|
2004
|
Vol. 52, nr 2
185-195
EN
Consistent theory is presented of continuum with defect distribution: dislocation and disclination densities and the densities of rotation nuclei of two kinds. Special attention is paid to rotation and twist motions, and the two approaches to the definition of the twist-bend tensor are combined. The elastic and self fields of stresses and strains become asymmetric, while the total fields remain symmetric as required by the compatibility conditions. However, the tensor of incompatibility becomes asymmetric. The dislocation-stress relations and the equations of motion for symmetric and asymmetric parts of stresses are given and the wave equations for spin and twist are derived. Some applications are shortly discussed.
19
Symplectic and time reversible integrator for rigid bodies
Kamberaj H., Low R.J., Neal M.P.
Systems Science
|
2003
|
Vol. 29, nr 2
31-45
EN
A symplectic and time-reversible molecular dynamics algorithm is presented for rigid molecules in the quaternion representation. The algorithm is developed on the basis of the Trotter factorisation scheme using a Hamiltonian formalism The structure is similar to that of the velocity Verlet algorithm. Subsequently we describe the coupling of the rigid bodies to a thermostat. The isothermal molecular dynamics is defined by introducing additional pseudo-friction coefficients, according to a generalised Nose-Hoover prescription.
20
Content available remote Checking the correctness of numerical solutions to equations of motion
Strzałko J.
Mechanics and Mechanical Engineering
|
1999
|
Vol. 3, nr 1
57--76
EN
A method for checking the correctness of numerical solutions to equations of motion for conservative and non-conservative mechanical systems expressed in terms of generalised coordinates has been presented. The suggested method consists in checking the energy level in a system under consideration. An application of the verification method of the solving procedure in numerical computations consists in supplementing equations of motion with an additional differential equation describing changes in the total energy and in tracing time histories of the balance of the energy supplied to the system, produced and dissipated in it, as well as the energy transferred to the surroundings. The equation of the energy balance changes is written by means of a certain function, whose derivative fulfils the condition C(t)=0. The solution accuracy is shown by a time history of the function C(t), which should remain constant versus time. A way the function C(t) is derived for holonomic systems described by Lagrange's equations of the second kind, for systems with kinematic constraints described by Lagrange's equations of the second kind with Lagrange multipliers, as well as by Maggi's equations and canonical equations, is given. The examples of applications presented concern, first of all, models of engineering machines.
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