Computational Reference Dynamical Model of a Multibody System With First Order Constraints

2017 ◽  
Author(s):  
Elżbieta Jarzębowska ◽  
Krzysztof Augustynek ◽  
Andrzej Urbaś
Keyword(s):  
Equations Of Motion ◽  
Computational Procedure ◽  
Dynamical Models ◽  
Constrained System ◽  
First Order ◽  
Performance Requirements ◽  
Control Goal ◽  
Order Constraints ◽  
Reaction Forces ◽  
And Control

The paper presents a development of a computational based procedure for generation of constrained system dynamical models. The constraints may be both holonomic and first order nonholonomic, either material or nonmaterial. The latter ones are referred to as programmed and they are imposed by a designer, a control engineer as a control goal, or may come from controlled system performance requirements. The procedure for generation of constrained dynamics provides then reference dynamical models, i.e. models whose solutions satisfy all the constraints put upon them. These models may serve as motion planners for control. The distinctions between the presented approach and the ones reported in the literature are that the constraints may be material or nonmaterial and the final equations of motion are derived in the reduced state form, i.e. constraint reaction forces are eliminated at the equations derivation level but not afterwards as in the case of the Lagrange approach. This is the essential advantage of our approach and this one computational procedure may serve both reference and control oriented dynamical models derivation. The procedure is applied to a manipulator model whose end effector is subjected to a programmed constrained.

Paper 5. Directional Stability and Control of a Vessel in Restricted Waters

1972 ◽  
Vol 14 (7) ◽  
pp. 29-33 ◽  
Author(s):  
M. Fujino
Keyword(s):  
Hydrodynamic Force ◽  
Equations Of Motion ◽  
Narrow Channel ◽  
Order Theory ◽  
Stability Criteria ◽  
First Order ◽  
Stability And Control ◽  
First Order Theory ◽  
And Control ◽  
Improve Stability

By way of introduction the paper discusses conflicting observations of stability behaviour of ships in restricted waters. The equations of motion of a ship in a narrow channel are given, leading to stability criteria; differences from the deep water case are highlighted. More qualitatively, the theory also illustrates the asymmetric hydrodynamic force. Criteria are outlined for an automatic control system to improve stability. However, the first-order theory is shown to provide an inadequate description of all experimental results.

A Unified Framework for Dynamics and Lyapunov Stability of Holonomically Constrained Rigid Bodies

2005 ◽  
Vol 9 (4) ◽  
pp. 387-394 ◽  
Author(s):  
Khoder Melhem ◽  
◽  
Zhaoheng Liu ◽  
Antonio Loría ◽  
◽  
...  
Keyword(s):  
System Dynamics ◽  
Lyapunov Stability ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Minimal Realization ◽  
State Variables ◽  
Unified Framework ◽  
Constrained System ◽  
And Control

A new dynamic model for interconnected rigid bodies is proposed here. The model formulation makes it possible to treat any physical system with finite number of degrees of freedom in a unified framework. This new model is a nonminimal realization of the system dynamics since it contains more state variables than is needed. A useful discussion shows how the dimension of the state of this model can be reduced by eliminating the redundancy in the equations of motion, thus obtaining the minimal realization of the system dynamics. With this formulation, we can for the first time explicitly determine the equations of the constraints between the elements of the mechanical system corresponding to the interconnected rigid bodies in question. One of the advantages coming with this model is that we can use it to demonstrate that Lyapunov stability and control structure for the constrained system can be deducted by projection in the submanifold of movement from appropriate Lyapunov stability and stabilizing control of the corresponding unconstrained system. This procedure is tested by some simulations using the model of two-link planar robot.

Fluid-Structure Interaction Forces at Pump-Impeller-Shroud Surfaces for Rotordynamic Calculations

1989 ◽  
Vol 111 (3) ◽  
pp. 216-225 ◽  
Author(s):  
D. W. Childs
Keyword(s):  
Equations Of Motion ◽  
Perturbation Expansion ◽  
Momentum Equation ◽  
Governing Equations ◽  
Pump Impeller ◽  
First Order ◽  
Pressure Distributions ◽  
Pump Housing ◽  
Reaction Forces ◽  
Ring Seal

Governing equations of motion are derived for a bulk-flow model of the leakage path between an impeller shroud and a pump housing. The governing equations consist of a path-momentum, a circumferential-momentum, and a continuity equation. The fluid annulus between the impeller shroud and pump housing is assumed to be circumferentially symmetric when the impeller is centered; i.e., the clearance can vary along the pump axis but does not vary in the circumferential direction. A perturbation expansion of the governing equations in the eccentricity ratio yields a set of zeroth and first-order governing equations. The zeroth-order equations define the leakage rate and the circumferential and path velocity distributions and pressure distributions for a centered impeller position. The first-order equations define the perturbations in the velocity and pressure distributions due to either a radial-displacement perturbation or a tilt perturbation of the impeller. Integration of the perturbed pressure and shear-stress distribution acting on the rotor yields the reaction forces and moments acting on the impeller face. Calculated results yield predictions of possible resonance peaks of the fluid within the annulus formed by the impeller shroud and housing. Centrifugal acceleration terms in the path-momentum equation are the physical origin of these unexpected predictions. For normalized tangential velocities at the inlet to the annulus, uθ0(0) = Uθ0(0)/Riω of 0.5, the phenomenon is relatively minor. As uθ0(0) is increased to 0.7, sharp peaks are predicted. Comparisons for rotordynamic coefficient predictions with test results of Bolleter et al. show reasonable agreement for cross-coupled stiffness and direct damping terms. Calculated results are provided which make comparisons between seal forces and shroud forces for a typical impeller/wear-ring-seal combination.

Human Motion Modeling With a Robotics Method: Analysis of a Person Riding a Bus

2008 ◽  
Author(s):  
Ashish D. Deshpande ◽  
Jonathan E. Luntz
Keyword(s):  
Equations Of Motion ◽  
Human Motion ◽  
Contact Forces ◽  
Body Motion ◽  
Control Analysis ◽  
Motion Modeling ◽  
Open Chain ◽  
Motion Models ◽  
Performance Requirements ◽  
And Control

Deriving models of human body motion is important for prosthetics, rehabilitation and development of humanoids. We present a method that simplifies the derivation of equations of motion of human movements. We illustrate our approach by deriving motion models of a person riding in a moving bus. Our approach simplifies the derivation of dynamics as only open chain dynamics are to be derived. The kinematic constraints are then introduced to represent a complete system model in which the contact forces appear explicitly. We then constrain the contact forces based on the performance requirements to determine the feasibility of motions, which is difficult to determine with the traditional methods. Our model allows for the design and control analysis, specifically, the derivation of the relationship between the change in rider’s posture and the feasibility of motions.

Dynamic Modeling and Control of an Electromechanical Control Actuation System

2017 ◽  
Author(s):  
Ümit Yerlikaya ◽  
R. Tuna Balkan
Keyword(s):  
Nonlinear Model ◽  
Equations Of Motion ◽  
Ball Screw ◽  
Loop Control ◽  
Modeling And Control ◽  
Performance Requirements ◽  
Actuation System ◽  
Lever Mechanism ◽  
Actuation Systems ◽  
And Control

Electromechanical actuators are widely used in miscellaneous applications in engineering such as aircrafts, missiles, etc. due to their momentary overdrive capability, long-term storability, and low quiescent power/low maintenance characteristics. This work focuses on electromechanical control actuation systems (CAS) that are composed of a brushless direct current motor, ball screw, and lever mechanism. In this type of CAS, nonlinearity and asymmetry occur due to the lever mechanism itself, saturation limits, Coulomb friction, backlash, and initial mounting position of lever mechanism. In this study, both nonlinear and linear mathematical models are obtained using governing equations of motion. By using the linear model, it is shown that employing a PI-controller for position and a P-controller for velocity will be sufficient to satisfy performance requirements in the inner-loop control of an electromechanical CAS. The unknown controller parameters and anti-windup coefficient are obtained by the Optimization Tools of MATLAB using nonlinear model. Results obtained from the nonlinear model and real-time unloaded and loaded tests on a prototype developed are compared to verify the nonlinear model.

Kinetic theory

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Distribution Function ◽  
Kinetic Theory ◽  
Liouville Equation ◽  
Vlasov Equation ◽  
Particle Distribution ◽  
Equations Of Motion ◽  
Poisson Brackets ◽  
Hamiltonian Form ◽  
First Order ◽  
Number Of Particles

This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equation. Finally, it discusses the Jeans equations, which are the equations obtained by taking various averages over velocities.

scholarly journals Horizon radiation reaction forces

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Walter D. Goldberger ◽  
Ira Z. Rothstein
Keyword(s):  
Black Hole ◽  
Equations Of Motion ◽  
Finite Size ◽  
Radiation Reaction ◽  
Effective Field ◽  
Compact Objects ◽  
Finite Size Effect ◽  
Binary Black Holes ◽  
Dissipative Effects ◽  
Reaction Forces

Abstract Using Effective Field Theory (EFT) methods, we compute the effects of horizon dissipation on the gravitational interactions of relativistic binary black hole systems. We assume that the dynamics is perturbative, i.e it admits an expansion in powers of Newton’s constant (post-Minkowskian, or PM, approximation). As applications, we compute corrections to the scattering angle in a black hole collision due to dissipative effects to leading PM order, as well as the post-Newtonian (PN) corrections to the equations of motion of binary black holes in non-relativistic orbits, which represents the leading order finite size effect in the equations of motion. The methods developed here are also applicable to the case of more general compact objects, eg. neutron stars, where the magnitude of the dissipative effects depends on non-gravitational physics (e.g, the equation of state for nuclear matter).

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