Distributed attitude synchronization for multiple rigid bodies with euler-lagrange equations of motion

2007 ◽  
Author(s):  
Wei Ren
Keyword(s):  
Equations Of Motion ◽  
Rigid Bodies ◽  
Lagrange Equations ◽  
Attitude Synchronization

Robust adaptive vibration control of an underactuated flexible spacecraft

2018 ◽  
Vol 25 (4) ◽  
pp. 834-850 ◽  
Author(s):  
H. MoradiMaryamnegari ◽  
A.M. Khoshnood
Keyword(s):  
Rigid Body ◽  
Vibration Control ◽  
Control Method ◽  
Frequency Estimation ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Lagrange Equations ◽  
Flexible Bodies ◽  
Robust Adaptive ◽  
Adaptive Vibration Control

Designing a controller for multi-body systems including flexible and rigid bodies has always been one of the major engineering challenges. Equations of motion of these systems comprise extremely nonlinear and coupled terms. Vibrations of flexible bodies affect sensors of rigid bodies and might make the system unstable. Introducing a new control strategy for designing control systems which do not require the rigid–flexible coupling model and can dwindle vibrations without sensors or actuators on flexible bodies is the purpose of this paper. In this study, a spacecraft comprising a rigid body and a flexible panel is used as the case study, and its equations of motion are extracted using Lagrange equations in terms of quasi-coordinates. For oscillations on a rigid body to be eliminated, a frequency estimation algorithm and an adaptive filtering are used. A controller is designed based on the rigid model of the system, and then robust stability conditions for the rigid–flexible system are obtained. The conditions are also developed for the spacecraft with more than one active frequency. Finally, the robust adaptive vibration control system is simulated in the presence of resonance. Simulations’ results indicate the advantage of the control method even when several active frequencies simultaneously resonate the dynamics system.

scholarly journals A least action principle for interceptive walking

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Soon Ho Kim ◽  
Jong Won Kim ◽  
Hyun Chae Chung ◽  
MooYoung Choi
Keyword(s):  
Social Systems ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Action Principle ◽  
Lagrange Equations ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Principle Of Least Action ◽  
Human Participants

AbstractThe principle of least effort has been widely used to explain phenomena related to human behavior ranging from topics in language to those in social systems. It has precedence in the principle of least action from the Lagrangian formulation of classical mechanics. In this study, we present a model for interceptive human walking based on the least action principle. Taking inspiration from Lagrangian mechanics, a Lagrangian is defined as effort minus security, with two different specific mathematical forms. The resulting Euler–Lagrange equations are then solved to obtain the equations of motion. The model is validated using experimental data from a virtual reality crossing simulation with human participants. We thus conclude that the least action principle provides a useful tool in the study of interceptive walking.

Adaptive neural-based finite-time attitude synchronization and tracking control of multiple rigid bodies under actuator faults and saturation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Amin Mihankhah ◽  
Ali Doustmohammadi
Keyword(s):  
Finite Time ◽  
Tracking Control ◽  
Estimation Error ◽  
External Disturbance ◽  
Upper Bounds ◽  
Rigid Bodies ◽  
Sliding Surface ◽  
Actuator Faults ◽  
Content Type ◽  
Attitude Synchronization

Purpose The purpose of this paper, is to solve the problem of finite-time fault-tolerant attitude synchronization and tracking control of multiple rigid bodies in presence of model uncertainty, external disturbances, actuator faults and saturation. It is assumed that the rigid bodies in the formation may encounter loss of effectiveness and/or bias actuator faults. Design/methodology/approach For the purpose, adaptive terminal sliding mode control and neural network structure are used, and a new sliding surface is proposed to guarantee known finite-time convergence not only at the reaching phase but also on the sliding surface. The sliding surface is then modified using a proposed auxiliary system to maintain stability under actuator saturation. Findings Assuming that the communication topology between the rigid bodies is governed by an undirected connected graph and the upper bounds on the actuators’ faults, estimation error of model uncertainty and external disturbance are unknown, not only the attitudes of the rigid bodies in the formation are synchronized but also they track the time-varying attitude of a virtual leader. Using Lyapunov stability approach, finite-time stability of the proposed control algorithms demonstrated on the sliding phase as well as the reaching phase. The effectiveness of the proposed algorithm is also validated by simulation. Originality/value The proposed controller has the advantage that the need for any fault detection and diagnosis mechanism and the upper bounds information on estimation error and external disturbance is eliminated.

Effect of Material and Geometric Parameters on the Steady-State Belt Stresses and Belt Slip for Flat Belt-Drives

2015 ◽  
Author(s):  
Cagkan Yildiz ◽  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Flexible Multibody Dynamics ◽  
Friction Model ◽  
Rigid Bodies ◽  
Geometric Parameters ◽  
Rubber Matrix ◽  
Axial Stiffness ◽  
Belt Drive

In order to accurately predict the fatigue life and wear life of a belt, the various stresses that the belt is subjected to and the belt slip over the pulleys must be accurately calculated. In this paper, the effect of material and geometric parameters on the steady-state stresses (including normal, tangential and axial stresses), average belt slip for a flat belt, and belt-drive energy efficiency is studied using a high-fidelity flexible multibody dynamics model of the belt-drive. The belt’s rubber matrix is modeled using three-dimensional brick elements and the belt’s reinforcements are modeled using one dimensional truss elements. Friction between the belt and the pulleys is modeled using an asperity-based Coulomb friction model. The pulleys are modeled as cylindrical rigid bodies. The equations of motion are integrated using a time-accurate explicit solution procedure. The material parameters studied are the belt-pulley friction coefficient and the belt axial stiffness and damping. The geometric parameters studied are the belt thickness and the pulleys’ centers distance.

scholarly journals A Simulation Model for Computing the Loads Generated at Landing Site During Helicopter Take-Off or Landing Operation

2019 ◽  
Vol 2019 (2) ◽  
pp. 59-75
Author(s):  
Jarosław Stanisławski
Keyword(s):  
Equations Of Motion ◽  
Landing Site ◽  
Simulation Method ◽  
Rigid Bodies ◽  
Landing Gear ◽  
Rotor Blades ◽  
Wind Gust ◽  
The Galerkin Method ◽  
Lumped Masses ◽  
And Control

Summary The paper presents simulation method and results of calculations determining behavior of helicopter and landing site loads which are generated during phase of the helicopter take-off and landing. For helicopter with whirling rotor standing on ground or touching it, the loads of landing gear depend on the parameters of helicopter movement, occurrence of wind gusts and control of pitch angle of the rotor blades. The considered model of helicopter consists of the fuselage and main transmission treated as rigid bodies connected with elastic elements. The fuselage is supported by landing gear modeled by units of spring and damping elements. The rotor blades are modeled as elastic axes with sets of lumped masses of blade segments distributed along them. The Runge-Kutta method was used to solve the equations of motion of the helicopter model. According to the Galerkin method, it was assumed that the parameters of the elastic blade motion can be treated as a combination of its bending and torsion eigen modes. For calculations, data of a hypothetical light helicopter were applied. Simulation results were presented for the cases of landing helicopter touching ground with different vertical speed and for phase of take-off including influence of rotor speed changes, wind gust and control of blade pitch. The simulation method may help to define the limits of helicopter safe operation on the landing surfaces.

Simulation of Planar Dynamic Mechanical Systems With Changing Topologies: Part I — Characterization and Prediction of the Kinematic Constraint Changes

1987 ◽  
Author(s):  
B. J. Gilmore ◽  
R. J. Cipra
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Rigid Bodies ◽  
State Variables ◽  
Kinematic Constraint ◽  
Kinematic Constraints ◽  
Force Closure ◽  
Simulation Strategy ◽  
Reaction Forces ◽  
Discontinuous Equations

Abstract Due to changes in the kinematic constraints, many mechanical systems are described by discontinuous equations of motion. This paper addresses those changes in the kinematic constraints which are caused by planar bodies contacting and separating. A strategy to automatically predict and detect the kinematic constraint changes, which are functions of the system dynamics, is presented in Part I. The strategy employs the concepts of point to line contact kinematic constraints, force closure, and ray firing together with the information provided by the rigid bodies’ boundary descriptions, state variables, and reaction forces to characterize the kinematic constraint changes. Since the strategy automatically predicts and detects constraint changes, it is capable of simulating mechanical systems with unpredictable or unforeseen changes in topology. Part II presents the implementation of the characterizations into a simulation strategy and presents examples.

Elements of Classical Field Theory

2021 ◽  
pp. 24-34
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Field Theory ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Classical Field Theory ◽  
Classical Field ◽  
Lagrange Equations ◽  
Lie Group Of Transformations ◽  
Infinitesimal Transformations ◽  
Conserved Currents

The purpose of this chapter is to recall the principles of Lagrangian and Hamiltonian classical mechanics. Many results are presented without detailed proofs. We obtain the Euler–Lagrange equations of motion, and show the equivalence with Hamilton’s equations. We derive Noether’s theorem and show the connection between symmetries and conservation laws. These principles are extended to a system with an infinite number of degrees of freedom, i.e. a classical field theory. The invariance under a Lie group of transformations implies the existence of conserved currents. The corresponding charges generate, through the Poisson brackets, the infinitesimal transformations of the fields as well as the Lie algebra of the group.

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