Accuracy of Linearization Methods

2008 ◽  
pp. 341-376 ◽  
Author(s):  
Leslaw Socha
Keyword(s):  
Linearization Methods

scholarly journals Assessment of Linearization Approaches for Multibody Dynamics Formulations

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Francisco González ◽  
Pierangelo Masarati ◽  
Javier Cuadrado ◽  
Miguel A. Naya
Keyword(s):  
Mechanical System ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Practical Applications ◽  
Linearization Methods ◽  
Highly Nonlinear ◽  
Wide Range ◽  
The Way

Formulating the dynamics equations of a mechanical system following a multibody dynamics approach often leads to a set of highly nonlinear differential-algebraic equations (DAEs). While this form of the equations of motion is suitable for a wide range of practical applications, in some cases it is necessary to have access to the linearized system dynamics. This is the case when stability and modal analyses are to be carried out; the definition of plant and system models for certain control algorithms and state estimators also requires a linear expression of the dynamics. A number of methods for the linearization of multibody dynamics can be found in the literature. They differ in both the approach that they follow to handle the equations of motion and the way in which they deliver their results, which in turn are determined by the selection of the generalized coordinates used to describe the mechanical system. This selection is closely related to the way in which the kinematic constraints of the system are treated. Three major approaches can be distinguished and used to categorize most of the linearization methods published so far. In this work, we demonstrate the properties of each approach in the linearization of systems in static equilibrium, illustrating them with the study of two representative examples.

Computation of Wave Added Resistance by Control Surface Integration

2016 ◽  
Author(s):  
Zhiyuan Pan ◽  
Torgeir Vada ◽  
Kaijia Han
Keyword(s):  
Free Surface ◽  
Near Field ◽  
Momentum Conservation ◽  
Ship Hull ◽  
Control Surface ◽  
Floating Body ◽  
Added Resistance ◽  
Time Step ◽  
Rankine Source ◽  
Linearization Methods

A time domain Rankine source solver is extended to compute the wave added resistance of ships. The proposed approach applies the momentum conservation principle on the near field fluid volume enclosed by the wet surface of a floating body, the free surface and a control surface. The wave added resistance is then calculated by the integration over the control surface of the fluid velocities and free surface elevations. To be able to incorporate the proposed method with the Rankine source code, an interpolation scheme has been developed to compute the kinematics for the off-body points close to (or on) the free surface. Two Wigley ship models, a containership model S175 and a tanker model KVLCC2 are used to validate the present method. In general good agreement is found comparing with the model test data. The convergence behavior is examined for the proposed method including the selection of the time step and location of the control surface. Both Neumann-Kelvin and double body linearization methods are evaluated with the proposed method. It is found that the Neumann-Kelvin linearization can only be applied for slender ship hull, whereas double body method fits also for blunt ships. It is suggested to apply the proposed method with double body linearization to evaluate the wave added resistance of ships with a control surface close to the ship hull.

scholarly journals Study on non-stationary heat exchange in combined packages of water-resistant protective clothing of firefighters

2020 ◽  
Vol 64 (4) ◽  
pp. 467-476
Author(s):  
A. I. Ol’shanskii ◽  
R. V. Okunev ◽  
A. M. Gusarov
Keyword(s):  
Thermal Conductivity ◽  
Heat Exchange ◽  
Protective Clothing ◽  
Thermal Contact ◽  
Exchange Process ◽  
Toxic Substances ◽  
Nonlinear Transport ◽  
Stationary Heat ◽  
Technical Requirements ◽  
Linearization Methods

The results of research of non-stationary heat exchange in combined packages intended for creation of special water- and heat-resistant protective clothing of firefighters from dangerous and harmful factors during emergency rescue and other urgent works, with participation of non-toxic substances, acid solutions, alkalis, oil and petroleum products, liquid toxic substances, as well as during operation in water with temperature from 0 to 70 °С are presented. The stability of clothing material packs has been investigated as a transient heat exchange process in a multilayer plate with ideal thermal contact at the joints of the layers. The unlimited plate is heated on both sides under different heat exchange conditions according to Newton’s Law, with constant action of the heat source on one of the surfaces of the hot liquid contacting through the waterproof thin surface. Second surface of the plate interacts with external medium, temperature of which varies according to linear law. At solving the equation of non-stationary thermal conductivity with nonlinear transport coefficients, linearization methods are used based on the approximation of nonlinear coefficients, such that nonlinear equations become approximately linear. The entire heat transfer process is divided into a plurality of small-time intervals within which the transfer coefficients are constant. The zonal method of investigation of non-stationary thermal conductivity in clothing packages establishes equations for calculation of temperature, densities of thermal flows, distribution of temperature across thickness of clothing packages. It has been shown that under accepted calculation simplifications, parameter values are well consistent with the experiment. The composition of the clothing package is proposed, which meets the technical requirements of TУ BY 101114857.082-2015 “Personal Protective Kits”.

Convolution Estimates and Generalized de Leeuw Theorems for Multipliers of Weak Type (1,1)

1995 ◽  
Vol 47 (2) ◽  
pp. 225-245
Author(s):  
Nakhlé Asmar ◽  
Earl Berkson ◽  
T. A. Gillespie
Keyword(s):  
Abelian Group ◽  
Weak Type ◽  
Full Range ◽  
Locally Compact Abelian Group ◽  
Strong Type ◽  
Locally Compact ◽  
Linearization Methods ◽  
Maximal Theorem ◽  
Abstract Setting ◽  
Central Result

AbstractIn the context of a locally compact abelian group, we establish maximal theorem counterparts for weak type (1,1) multipliers of the classical de Leeuw theorems for individual strong multipliers. Special methods are developed to handle the weak type (1,1) estimates involved since standard linearization methods such as Lorentz space duality do not apply to this case. In particular, our central result is a maximal theorem for convolutions with weak type (1,1) multipliers which opens avenues of approximation. These results complete a recent series of papers by the authors which extend the de Leeuw theorems to a full range of strong type and weak type maximal multiplier estimates in the abstract setting.

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