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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
131

Analýza stability řezného procesu obráběcího stroje vzhledem k samobuzenému kmitání / STABILITY ANALYSIS OF CUTTING PROCESS OF MACHINE TOOL WITH RESPECT TO CHATTER

Vetiška, Jan January 2013 (has links)
The thesis deals with building and utilization of mechatronic models which are based on modeling of system of rigid and flexible bodies. Such models are then used for analysis of behavior of complex systems, for instance machine tools. The work is concentrated on analysis of self-excitation of a machine tool. The appearance of the self-excitation during the machining may be influenced by several methods described in the work. The evaluation of the appearance of the self-excitation is analyzed via so called lobe diagram. It is necessary to know transfer function describing the impact of acting forces on the deformation of the system (machine tool in this case) for compilation of the lobe diagram. The whole structure of the model shows compliant behavior which dramatically influences the transfer function thus the approach to the modeling of mechanical parts as flexible bodies is proposed. There are created models of modally reduced flexible bodies based on modified CAD models which have same modal properties as non-reduced FEM models up to the maximal excitation frequency. The reduced models have significantly lower number of degrees of freedom and it is possible to work with them in multi-body simulation tools and at the same time they contain the information about the deformations. The work utilizes Graig-Bamton method which is implemented to the ANSYS. The whole model is consequently built and analyzed in ADAMS. It is possible to export the linearized model of the system in form of state matrices which are used for writing of the transfer function. The conditions of stability of the machining process are then evaluated via the lobe diagram. The proposed thesis presents the modeling of mechatronic systems with stiff and rigid bodies. The approach may be used for analysis of machining tools as well as for development of advanced mechatronic systems with active damping, etc.
132

Simulace kinematiky a dynamiky vozidlových mechanismů / Vehicle Kinematics and Dynamics Simulations

Zháňal, Lubor January 2015 (has links)
This paper focuses on the kinematic and dynamic numerical simulation of mechanisms by applying a numerical method, and a complex simulation programme built on it, developed by the author. Described are mathematical principles of the numerical method used and also the programming progression of the important parts of the application and its optimization. The final part includes comparative measuring of the accuracy and performance.
133

Learning a Grasp Prediction Model for Forestry Applications

Olofsson, Elias January 2024 (has links)
Since the advent of machine learning and machine vision methods, progress has been made in tackling the long-standing research question of autonomous grasping of arbitrary objects using robotic end-effectors. Building on these efforts, we focus on a subset of the general grasping problem concerning the automation of a forwarder. This forestry vehicle collects and transports felled and cut tree logs in a forest environment to a nearby roadside landing. The forwarder must safely and energy-efficiently grip logs to minimize fuel consumption and reduce loading times. In this thesis project, we develop a data-driven model for predicting the expected outcome of grasping attempts made by the forwarder's crane. For a given pile of logs, such a model can estimate the optimal horizontal location and angle for applying the claw grapple, enabling effective grasp planning. We utilize physics-based simulations to create a ground truth dataset of 12 500 000 simulated grasps distributed across 5000 randomly generated log piles. Our semi-generative, supervised model is a fully convolutional network that inputs the orthographic depth image of a pile and returns images predicting the corresponding grasps' initial grapple angle and outcome metrics as a function of position. Over five folds of cross-validation, our model predicted the number of grasped logs and the initial grapple angle with a normalized root mean squared error of 15.77(2)% and 2.64(4)%, respectively. The grasps' energy efficiency and energy waste were similarly predicted with a relative error of 14.43(2)% and 21.06(3)%. / Sedan tillkomsten av maskininlärnings- och maskinseendebaserade metoder har betydande framsteg gjorts inom forskningsområdet för autonom greppning av godtyckliga objekt med en robotisk sluteffektor. Vi bygger vidare på dessa resultat och fokuserar på en del av det generella greppningsproblemet gällande automatisering av en skotare. Denna skogsmaskin samlar in och transporterar fällda och kapade trädstammar från avverkningsplats till upplag intill närliggande skogsbilväg. Skotaren måste greppa och lyfta stockarna på ett säkert och energieffektivt sätt för att minimera bränsleförbrukningen samt minska lastningstiderna. I detta examensarbete utvecklar vi en datadriven modell för att förutsäga det förväntade resultatet av gripförsök utförda av skotarens kran. För en given timmerstockshög kan en sådan modell uppskatta den optimala positionen och vinkeln för att applicera skotarens gripklo, vilket möjliggör effektiv planering av lastningen. Vi använder fysikbaserade simuleringar för att skapa ett dataset med 12 500 000 simulerade gripförsök fördelade över 5000 slumpmässigt genererade timmerhögar. Vår semi-generativa, övervakade modell är ett djupt faltningsnätverk utan helt sammankopplade neuronlager som tar in en ortografisk djupbild av en timmerhög och returnerar bilder som predikterar de motsvarande gripförsökens initiala gripvinkel och resultatmått som en funktion av position. Vid en femfaldig korsvalidering förutsåg vår modell antalet greppade stockar och den initiala gripvinkeln med ett normaliserat rotmedelkvadratfel på 15.77(2)% respektive 2.64(4)%. Gripförsökens energieffektivitet och energiförlust predikterades på liknande sätt med ett relativt fel på 14.43(2)% och 21.06(3)%.
134

Multibody modelling of the vibrations in an aircraft engine / Flerkroppsmodellering av vibrationerna i enflygplansmotor

Mollet, Charly January 2022 (has links)
During the assembly of aircraft engines, some clearance is left in the rolling bearings mainly to reduce friction. However this clearance might allow the rolling element to vibrate during flight. Indeed, unwanted vibrations called non-synchronous vibrations (NSV) appear on the data recorded by the sensors on some development engines. NSV can be dangerous for the engine so they are closely monitored.  To prevent the appearance of the NSV, they are investigated by the engineers as soon as they appear during tests. The main source of the NSV is most likely to be the rolling bearings in the rotor because they induce a non-linear behaviour. The bearings of development engines were investigated on Finite Element Method (FEM) software for example but other methods could bring a contribution for the understanding of the NSV.  In this study, a multibody modelling software is used to try to model and explain the observed sub-synchronous vibrations considered as NSV. A model of the rotor of a prototype engine on a FEM software is provided and then reduced to be implemented in the new software. The behaviour of this new model is tested through modal analysis and response to imbalance.  Once the model is properly set, a parametric study is performed to see the effect of the thrust, gravity, imbalance weight and clearance on the system. It shows that clearance and gravity are key parameters while thrust and the imbalance weight have a minor impact on the NSV. This study has also helped to fix the parameters used to reproduce the NSV observed in the experiments.  Then, a second study focus on the influence of the clearance of the roller bearings on the NSV. This study defines a range of clearance that can be implemented on the engine to avoid the NSV. It also proved that the vibrations were very sensitive to a small change in the clearance values.  Finally, by studying the previous configurations, a link between the stiffness of the bearing and the occurrence of the NSV was established. In fact, the NSV appear only when the two roller bearings both have no stiffness because the clearance is not filled by the radial load. The rolling element is thus free to vibrate in its ring. It was noticed that the NSV has more chance to occur if it has already come out earlier in the run-up of the engine.  The multibody software is therefore perfectly able to reproduce the vibrations in a rotor. It is now a tool that can be used during the development process. / Vid montering av flygplansmotorer lämnas ett spelrum i rullningslagren främst för att minska friktionen. Detta spelrum kan emellertid tillåta att rullelementet vibrerar under flygning. Faktum är att oönskade vibrationer som kallas non-synchronous vibrations (NSV) visas på data som registreras av sensorerna på utveckling motorerna. NSV kan vara farligt för motorn och övervakas därför noggrant.För att förhindra uppkomsten av NSV utreds de regelbundet av ingenjörerna. Den huvudsakliga källan till NSV är troligen rullager i rotorn eftersom de inducerar ett icke-linjärt beteende. Lagren för utveckling motorer undersöktes till exempel med Finita Element-metoden (FEM) programvara men andra metoder skulle kunna bidra till förståelsen av NSV. I denna studie används en multibody-modelleringsprogramvara för att försöka modellera och förklara de observerade subsynkrona vibrationerna som betraktas som NSV. En modell av rotorn till en utveckling motor tillhandahålls i ett FEM-program och reduceras sedan för att implementeras i den nya mjukvaran. Beteendet hos denna nya modell testas genom modal analys och respons på obalans. När modellen är inställd utförs en parametrisk studie för att se effekten av dragkraften, gravitationen, obalansvikten och frigången i systemet.Den visar att frigång och gravitation är nyckelparametrar medan dragkraft och obalansvikt har en mindre inverkan på NSV. Denna studie har också hjälpt till att bestämma de parametrar som används för att reproducera NSV som observerats i experimenten. Därefter fokuserar en andra studie på inverkan av rullagernas frigång på NSV. Denna studie definierar ett intervall av spelrum som kan implementeras på motorn för att undvika NSV. Det visade sig också att vibrationerna var mycket känsliga för en liten ändring av frigångsvärdena.Slutligen, genom att studera de tidigare konfigurationerna, etablerades en koppling mellan lagrets styvhet och förekomsten av NSV. Faktum är att NSV endast visas när de två rullagren båda inte har någon styvhet eftersom spelet inte fylls av den radiella belastningen. Rullelementet är således fritt att vibrera i sin ring. Det märktes att NSV har större chans att inträffa om den redan sker tidigare i motorns start. Multibody-mjukvaran är därför perfekt för att reproducera vibrationerna i en rotor. Det är nu ett verktyg som kan användas under utvecklingsprocessen.
135

Car seat design and human-body modelling for rear impact whiplash mitigation

Himmetoglu, Selcuk January 2008 (has links)
Whiplash is a neck injury caused by the sudden differential movement between the head and torso. Whiplash injuries are most commonly reported as a consequence of rear impacts in car accidents. They are regarded as minor injuries, but can still lead to long-term disablement and discomfort in the neck. Whiplash injuries can be mitigated by better car seat designs. For this purpose, head restraint geometry must be improved first, and then the dynamic performance of the whole seat must be assessed at all crash seventies. A biofidelic human-body model is a key requirement in designing whiplash mitigating car seats. This thesis presents the development of a 50th percentile male multi-body human model and several energy absorbing car seat designs. The human-body model is specifically designed for rear impact and validated using the responses of seven volunteers from Japanese Automobile Research Institute (JARI) sled tests, which were performed at an impact speed of 8 kph with a rigid seat and without head restraint and seat belt. A generic multi-body car seat model is also developed to implement various seatback and recliner properties, anti-whiplash devices (A WDs) and head restraints. Using the same driving posture and the rigid seat in the JARI sled tests as the basic configuration, several anti-whiplash seats are designed to allow different types of motion for the seatback and seat-pan. The major findings of this research are: -The human-body model simulates the effects of muscle contraction and its overall response is superior in comparison to the currently used models and dummies. -A criterion called the S-shape index (SSI) is developed based on the intervertebral angles of the upper and lower cervical spine. -The car seat design concepts are able to control and use crash energy effectively with the aid of anti-whiplash devices for a wide range of crash seventies. -In order to reduce whiplash injury risk, this study advocates energy absorbing car seats which can also provide head restraint contact as early as possible.
136

Mehrkörpersimulation eines ebenen Koppelgetriebes mittels Matlab / ADAMS -Co-Simulation / Multibody simulation of a planar 5 Bar mechanism with Matlab/ADAMS-Co- Simulation

Gollee, Christian, Troll, Clemens 06 June 2017 (has links) (PDF)
Mit Hilfe der Matlab/ADAMS-Co-Simulation wird ein ebenes Koppelgetriebe (5- Gelenk) untersucht und anschließend die Wirkpaarung mit einem Stückgut betrachtet. Dabei werden verschiedene Modellierungsstufen angewendet und die Simulationsergebnisse Messergebnissen vom Versuchsstand gegenübergestellt. Daneben wird die grundlegende Herangehensweise beim Einsatz dieser Simulationswerkzeuge erläutert.
137

Estudo da influência da rigidez do quadro na dirigibilidade de um veículo de competição Fórmula SAE em ambiente multicorpos / Study of the influence of the frame stiffness in handling with a Formula SAE vehicle in multibody interface

Ericsson, Luis Gustavo Sigward 19 December 2008 (has links)
O objetivo deste trabalho é estudar a influência da rigidez do quadro na dirigibilidade de um veículo de competição fórmula SAE (protótipo E2-M, da equipe EESC-USP) em ambiente multicorpos com o software Adams/Car. Um modelo contendo os subsistemas de suspensão, direção, pneumático, powertrain, barra estabilizadora e quadro foi construído em ambiente multicorpos com componentes modelados como corpos rígidos. Posteriormente foram elaborados três modelos de quadros flexíveis com diferentes valores de rigidez torcional para substituir o quadro rígido. Estes foram obtidos através da análise modal com o auxílio do método dos elementos finitos. Para comparação da dinâmica lateral dos modelos, típicas manobras do estudo de dirigibilidade foram consideradas tais como rampsteer, step-steer e single lane change. Os resultados obtidos foram de aceleração lateral e velocidade de guinada. Pelas condições avaliadas, pode-se concluir que a rigidez torcional de um quadro para o protótipo E2-M pode estar entre 700 e 1500 N.m/o. Essa variação de rigidez representou 5 kg de massa no quadro. Porém deve-se fazer uma avaliação modal com a massa suspensa calibrada para verificar se não existe acoplamento de modos e freqüências com outros subsistemas. / This dissertation is intended to study the influence of frame stiffness in handling of a Formula SAE vehicle (E2-M prototype from EESC-USP Formula SAE team) in multibody with Adams/Car software. A model containing the subsystems of suspension, steering, tires, powertrain, frame and stabilizing bar was built considering rigid bodies. Subsequently, three models of flexible frames were developed with different values of torsional stiffness to replace the rigid frame. They were obtained through modal analysis with the aid of finite element method. For the handling investigation, maneuvers such as ramp-steer, step-steer and single lane change were considered. The results evaluated were lateral acceleration and yaw velocity. According to results, the torsional stiffness for the E2-M prototype can be between 700 and 1500 Nm/o. But an eigenvalue analyses is also necessary to verify if there is no coupling of modes of the calibrated sprung mass with other subsystems.
138

Modelagem de vagão ferroviário em sistema multicorpos e avaliação do comportamento dinâmico em via tangente com desnivelamento transversal periódico / Multibody system modelling of a railway freight car and dynamic analysis on tangent track with periodic cross level defect

Grando, Denilson 29 October 2012 (has links)
Este trabalho utiliza a técnica de modelagem de sistemas multicorpos para analisar o comportamento dinâmico de um vagão ferroviário de carga, trafegando sobre via tangente com desnivelamento transversal periódico. O estudo exibe a modelagem dos principais vínculos deste sistema, como o contato entre o prato e o pião, molas helicoidais e sistema de amortecimento de atrito seco da suspensão primária. A modelagem do contato entre o prato e o pião sugerida, é baseada em um modelo de elastic foundation, e utiliza a característica geométrica dos corpos em contato. O modelo dinâmico de atrito desenvolvido possui atuação bidirecional, sendo utilizado nos elementos dissipativos da suspensão. A matriz de rigidez das molas helicoidais da suspensão primária é obtida utilizando o Triedro de Frenet-Serret e o Segundo Teorema de Castigliano. O modelo matemático, confeccionado com a ferramenta de modelagem ADAMS/Rail, é composto por 90 corpos rígidos e uma caixa flexível e possui 210 graus de liberdade. A comparação dos resultados obtidos na identificação modal experimental e nas análises do modelo comprovou que as hipóteses adotadas na modelagem são aceitáveis, reforçando a utilização dos modelos multicorpos na análise dinâmica do veículo guiado. A variação da velocidade de tráfego do veículo, sobre diferentes comprimentos de irregularidade da via, proporcionou os resultados para confecção dos mapas de resposta dinâmica. Esses mapas foram traçados para o ângulo rolagem, alívio das forças no contato roda-trilho e razão L/V no rodeiro de ataque, e identificaram as regiões mais sensíveis para a rolagem harmônica. A rolagem e torção da caixa foram identificados como os movimentos principais do veículo, quando em tráfego em via com desnivelamento transversal periódico. O conjunto de prato e pião gasto aumentou a faixa de velocidade indicada como crítica para a rolagem, piorando os resultados para velocidades mais baixas. O aumento do amortecimento da suspensão primária, por meio da inclinação do lenoir link, diminuiu os valores de rolagem e do alívio em comparação ao caso nominal. A utilização do ampara-balaço de contato constante propiciou a diminuição do ângulo de rolagem, alívio das forças e da razão L/V do rodeiro na região de ressonância. O aumento do amortecimento deste vínculo, devido à mola elastomérica, proporcionou resultados ainda melhores e indicou que a alteração das características da suspensão secundária pode reduzir a amplitude do movimento de rolagem harmônica. A metodologia de análise do comportamento dinâmico proposta, através dos mapas de resposta, pode auxiliar na determinação das faixas críticas de velocidade de um vagão ferroviário de carga, no tráfego em vias cujas características típicas das irregularidades são conhecidas. Empresas do setor ferroviário podem aplicar este método no projeto de novos vagões, bem como no estudo da velocidade crítica de determinada frota já em operação. / This study uses the multibody system modeling techniques to analyze the dynamic behavior of a railway freight wagon, traveling over tangent track with periodic cross level defect. The study shows the modeling of the main links of the system, as the center plate contact, helical springs and dry friction damper. The suggested modeling of the center plate contact is based on an elastic foundation model, and uses the geometric characteristic of these bodies. The dynamic friction model developed is bidirectional, being used in the dissipative suspension elements. The stiffness matrix of the helical springs is obtained using the Frenet-Serret trihedral and the Second Castigliano Theorem. The mathematical model, developed with the software ADAMS/Rail, is composed of 90 rigid bodies and a flexible car body and has 210 degrees of freedom. A comparison of results obtained in experimental modal identification and analysis of the mathematical model showed that the assumptions made in modeling are acceptable, reinforcing the use of multibody models in dynamic analysis of rail vehicles. The traffic speed variation on different lengths of track irregularity provided the results to make the dynamic response maps. These maps were drawn to roll angle, vertical force in the wheel-rail contact and wheelset L/V and identified the most sensitive regions to harmonic roll. The roll and torsion of the car body were identified as the main movements of the vehicle, when traveling over tangent track with periodic cross level defect. The use of worn center plate increased the critical speed range to the roll motion and decreases the performance for slower speeds. The increase in the damping of the primary suspension, through the lenoir link inclination, decreased the rolling angle and wheel lift in comparison to the nominal case. The use of constant contact side bearer reduced the roll angle and wheelset L/V ratio and increased the vertical load on wheels in the resonance region. The use of elastomeric side bearer provided even better results indicating that changes of the secondary suspension characteristics can minimize the movement of harmonic roll. The methodology for analyzing the dynamic behavior, through the proposed response maps, can assist in determining the critical speed ranges of a railway freight wagon running over a track whose typical irregularities characteristics are known. Companies in the rail industry can apply this method in the design of new cars, and study the critical velocity of a given railway fleet already in operation.
139

Estudo de dirigibilidade de veículos longos combinados / Handling study of heavy articulates vehicles

Vieira, Januário Leal de Moraes 22 June 2010 (has links)
Apresenta um modelo completo em sistemas multicorpos de uma combinação veicular formada por um cavalo mecânico e um semi-reboque para um estudo de dirigibilidade. O modelo multicorpos foi desenvolvido no MSC.Adams/Car e inclui a suspensão primária, sistema de direção, trem de força, modelo de pneu e um quadro flexível para o cavalo mecânico, e a suspensão primária, modelo de pneu e quadro rígido para o semi-reboque. A resposta dinâmica lateral de uma composição veicular depende das características combinadas de estabilidade direcional, dirigibilidade e interação pneu/pavimento da unidade motora e da unidade rebocada. Os parâmetros mais importantes em relação à dinâmica lateral dos veículos longos combinados são: a velocidade longitudinal, o concerning stiffness dos pneus da combinação veicular, as elasticidades dos sistemas de suspensão e esterçamento do cavalo mecânico, a localização, distribuição do carregamento e momento de inércia em guinada da unidade movida e transferência lateral de carga do veículo como um todo. O modelo foi validado no âmbito dos modos de vibração. As análises de dirigibilidade foram realizadas mediante execução de manobras de mudança simples de pista e de esterçamento com entrada rampa, no MSC.Adams/Car, para calcular métricas comumente utilizadas para avaliação da dinâmica lateral de veículos longos combinados como aceleração lateral, velocidade de guinada, offtracking dinâmico e o gradiente de esterçamento. Análises dos resultados mostraram a influência no tempo de resposta, em regime transitório, do cavalo quando atrelado ao semi-reboque e um comportamento sub-esterçante nas velocidades longitudinais simuladas. A combinação veicular utilizada para este estudo apresenta um comportamento direcional estável. / This work presents a complete multibody model of a heavy articulated vehicle with a tractor and a semitrailer for handling study purposes. The model had been developed on MSC.Adams/Car and includes primary suspension system, steering system, powertrain, tire model and a flexible frame for tractor, suspension system, tire model and a rigid frame for semitrailer. The lateral dynamics response of a heavy articulated vehicle depends on tractor/semitrailer combined characteristics of the directional stability, the manouverability and the tire/road interaction. The most important parameters concerning of the lateral dynamics of heavy articulated vehicles are: longitudinal velocity, combined tire cornering stiffness of vehicular composition, suspensions systems compliance and steering system compliance of tractor, location, load distribution and yaw moment of towing unit and vehicle overall lateral load transfer. The model was validated about modal shapes and frequencies vibrations. Handling analyses had performed with single lane change and ramp steer maneuvers simulation on MSC.Adams/Car to calculate common measures for heavy articulated vehicles lateral dynamics evaluation as lateral acceleration, yaw velocity, dynamic offtracking and understeer gradient. The results analyses showed that the towing unit influences on response of the tractor and an understeer behavior of all vehicular composition over longitudinal velocity range simulated. The heavy articulated vehicle used on this study shows a stable directional behavior.
140

Desenvolvimento de um modelo não linear de três graus de liberdade para a análise da dinâmica lateral de um ônibus com suspensão a ar / Development of a nonlinear three degrees of freedom model for lateral dynamic analysis of a bus with air spring suspension system

Prado, Marcelo 04 April 2003 (has links)
Os modelos simplificados de veículos são importantes em fases iniciais do projeto de um veículo, quando muitas características geométricas ainda não estão definidas. No caso de ônibus com sistema de suspensão a ar, os modelos encontrados na literatura não levam em conta efeitos da válvula niveladora de altura. Dois modelos de um ônibus foram desenvolvidos: um modelo não linear de veículo com três graus de liberdade e um modelo em sistema multicorpos com 109 graus de liberdade. Os dois modelos possuem sistema de suspensão a ar com a modelagem termodinâmica do bolsão com a válvula niveladora de altura. As equações do modelo não linear de três graus de liberdade foram construídas utilizando o conceito de derivativos de estabilidade. Para a validação dos modelos, foram realizados ensaios experimentais com o veículo e as seguintes grandezas foram medidas: aceleração lateral, velocidade em guinada, velocidade lateral, ângulo de escorregamento do veículo e ângulo de rolamento. Os resultados obtidos com os modelos foram validados experimentalmente. O comportamento do ângulo de rolamento do veículo devido ao sistema de suspensão a ar foi reproduzido nos dois modelos. Foi desenvolvida uma interface gráfica dentro do ambiente ADAMS para a geração automática de modelos simplificados. Os dados do veículo são inseridos através de uma interface gráfica com caixas de diálogo. Modelos simplificados de veículos são utilizados no controle da dinâmica do veículo. Neste tipo de aplicação, as equações do modelo não linear de três graus de liberdade são resolvidas em tempo real e podem servir como um modelo de referência para sistemas adaptativos de controle. / Simplified vehicle models are very important at the initial stages of vehicle development when all geometric data are not yet available. In the case of a bus with an air suspension system, the models you find in the literature does not taken into account the control leveling valve effects. Two bus models were developed: a nonlinear three degrees of freedom model and a multibody model with 109 degrees of freedom. Both models have thermodynamic air suspension system model with control leveling valve. The three degrees of freedom equations were built using the stability derivative concept. In order to validate the models, experimental tests were carried out and the following variables were measured: lateral acceleration, yaw velocity, sideslip angle and roll angle. The model results were validated against actual data. The roll angle behavior due to air suspension system was reproduced in both models. A graphic user interface for developing simplified vehicle model, based on the nonlinear three degrees of freedom model equations, was built using the ADAMS interface. All the data necessary for the model are introduced via dialog boxes. Simplified vehicle models can be used in vehicle dynamics control. In this kind of application, the three degrees of freedom equations can be solved in real time simulation and can be used as a reference model in adaptive control system, for instance.

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